Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
On state-dependant sampling for nonlinear controlled systems sharing limited computational resources
Alamir, Mazen
2007-01-01
21 pages. soumis à la revue "IEEE Transactions on Automatic Control"; International audience; In this paper, a framework for dynamic monitoring of sampling periods for nonlinear controlled systems is proposed. This framework is particularly adapted to the context of controlled systems sharing limited computational resources. The proposed scheme can be used in a cascaded structure with any feedback scheduling design. Illustrative examples are given to assess the efficiency of the proposed fram...
An Efficient Implementation of Non-Linear Limit State Analysis Based on Lower-Bound Solutions
DEFF Research Database (Denmark)
Damkilde, Lars; Schmidt, Lotte Juhl
2005-01-01
Limit State analysis has been used in design for decades e.g. the yield line theory for concrete slabs or slip line solutions in geotechnics. In engineering practice manual methods have been dominating but in recent years the interest in numerical methods has been increasing. In this respect...
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2002-01-01
of reinforced concrete slabs or the stability of slopes, and generally, whenever all information about the structure, except for the ultimate magnitude of the load set, is known. However, in the design of structures the situation is the opposite. Here the loads are known whereas the necessary dimensions......Limit analysis has been used for decades in civil and mechanical engineering practice as a means of analyzing structures of materials which with reasonable accuracy can be described as being rigid-perfectly plastic. Such materials include steel, concrete and soils. Traditionally, most attention has......, boundary conditions, material strengths, etc. must be determined in such a way that the structure is able to sustain the given loads. Thus, limit analysis embraces two different scenarios, one where everything except the maximal permissible load intensity is known, and one where all that is known...
SEMICLASSICAL LIMIT OF NONLINEAR SCHRODINGER EQUATION (Ⅱ)
Institute of Scientific and Technical Information of China (English)
张平
2002-01-01
In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schrodinger equation in small time. We prove that: the limits of the quantum density: pε =: |ψε|2, and the quantum momentum: Jε =: εIm(ψεψε) satisfy the compressible Euler equations before the formation of singularities in the limit system.
Optical limiter based on two-dimensional nonlinear photonic crystals
Belabbas, Amirouche; Lazoul, Mohamed
2016-04-01
The aim behind this work is to investigate the capabilities of nonlinear photonic crystals to achieve ultra-fast optical limiters based on third order nonlinear effects. The purpose is to combine the actions of nonlinear effects with the properties of photonic crystals in order to activate the photonic band according to the magnitude of the nonlinear effects, themselves a function of incident laser power. We are interested in designing an optical limiter based nonlinear photonic crystal operating around 1064 nm and its second harmonic at 532 nm. Indeed, a very powerful solid-state laser that can blind or destroy optical sensors and is widely available and easy to handle. In this work, we perform design and optimization by numerical simulations to determine the better structure for the nonlinear photonic crystal to achieve compact and efficient integrated optical limiter. The approach consists to analyze the band structures in Kerr-nonlinear two-dimensional photonic crystals as a function of the optical intensity. We confirm that these bands are dynamically red-shifted with regard to the bands observed in linear photonic crystals or in the case of weak nonlinear effects. The implemented approach will help to understand such phenomena as intensitydriven optical limiting with Kerr-nonlinear photonic crystals.
Central Limit Theorem for Nonlinear Hawkes Processes
Zhu, Lingjiong
2012-01-01
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
Limiting amplitudes of fully nonlinear interfacial tides and solitons
Aguiar-González, Borja; Gerkema, Theo
2016-08-01
A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.
Spin squeezing in nonlinear spin coherent states
Wang, Xiaoguang
2001-01-01
We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and...
Directory of Open Access Journals (Sweden)
A. N. Bokhan
2009-01-01
Full Text Available One of the most efficient means of over-voltage reduction in arcing ground short-circuits is an application of a nonlinear over-voltage limiter. It is necessary to take into account dynamic properties of the nonlinear over-voltage limiter in order to ensure authentic simulation of over-voltage in the network A dynamic model of the non-linear over-voltage limiter which takes a time lag constant τ into account during transition of the nonlinear over-voltage limiter into conducting state has been developed in the paper.
Limiting effects of geometrical and optical nonlinearities on the squeezing in optomechanics
Energy Technology Data Exchange (ETDEWEB)
Djorwé, P. [Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I (Cameroon); Nana Engo, S.G., E-mail: nanaengo@gmail.com [Laboratory of Photonics, Faculty of Science, University of Ngaoundéré (Cameroon); Talla Mbé, J.H.; Woafo, P. [Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I (Cameroon)
2013-08-01
In recent experiments, the re-thermalization time of the mechanical resonator is stated as the limiting factor for quantum applications of optomechanical systems. To explain the origin of this limitation, an analytical nonlinear investigation supported by the recent successful experimental laser cooling parameters is carried out in this work. To this end, the effects of geometrical and the optical nonlinearities on the squeezing are studied and are in a good agreement with the experimental results. It appears that highly squeezed state are generated where these nonlinearities are minimized and that high nonlinearities are limiting factors to reach the quantum ground state.
Nonlinear Interferometry via Fock State Projection
Khoury, G; Eisenberg, H S; Fonseca, E J S
2006-01-01
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Nonlinear Interferometry via Fock-State Projection
Khoury, G.; Eisenberg, H. S.; Fonseca, E. J. S.; Bouwmeester, D.
2006-05-01
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).OPEXFF1094-408710.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
Nonlinear self-flipping of polarization states in asymmetric waveguides
Zhang, Wen Qi; Monro, Tanya M; Afshar, V Shahraam
2012-01-01
Waveguides of subwavelength dimensions with asymmetric geometries, such as rib waveguides, can display nonlinear polarization effects in which the nonlinear phase difference dominates the linear contribution, provided the birefringence is sufficiently small. We demonstrate that self-flipping polarization states can appear in such rib waveguides at low (mW) power levels. We describe an optical power limiting device with optimized rib waveguide parameters that can operate at low powers with switching properties.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Nonlinear limits to the information capacity of optical fiber communications
Mitra, P P; Mitra, Partha P.; Stark, Jason B.
2000-01-01
The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be considered. The nonlinear nature of the propagation of light in optical fiber has made these limits difficult to elucidate. Here we obtain basic insights into the limits to the information capacity of an optical fiber arising from these nonlinearities. The key simplification lies in relating the nonlinear channel to a linear channel with multiplicative noise, for which we are able to obtain analytical results. In fundamental distinction to the linear additive noise case, the capacity does not grow indefinitely with increasing signal power, but has a maximal value. The ideas presented here have broader implications for other nonlinear information channels, such as those involved in sensory transduction in neurobiology. These have been often examined using additive noise linear cha...
Nonlinear phonon interferometry at the Heisenberg limit
Cheung, Hil F. H.; Patil, Yogesh Sharad; Chang, Laura; Chakram, Srivatsan; Vengalattore, Mukund
2016-05-01
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ 1 /√{ N}) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. Here, we realize a prominent example of such schemes, the so-called SU(1,1) interferometer, in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ 1 / N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. We describe how our work extends the optomechanical toolbox and how it presents new avenues for studies of optomechanical sensing and studies of nonequilibrium dynamics of multimode optomechanical systems. This work was supported by the DARPA QuASAR program through a grant from the ARO, the ARO MURI on non-equilibrium manybody dynamics and an NSF INSPIRE award.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
Lower Bound Limit Analysis Of Slabs With Nonlinear Yield Criteria
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2002-01-01
A finite element formulation of the limit analysis of perfectly plastic slabs is given. An element with linear moment fields for which equilibrium is satisfied exactly is used in connection with an optimization algorithm taking into account the full nonlinearity of the yield criteria. Both load...
Nonlinear optical properties and optical power limiting effect of Giemsa dye
Al-Saidi, Imad Al-Deen Hussein A.; Abdulkareem, Saif Al-Deen
2016-08-01
The nonlinear optical properties of Giemsa dye in chloroform solution for different concentrations and dye mixed with poly(methylmethacrylate) (PMMA) as a dye-doped polymer film were investigated using continuous wave (CW) low power solid-state laser (SSL) operating at wavelength of 532 nm as an excitation source. Using the single beam z-scan technique, the nonlinear refractive index (n2), the nonlinear absorption coefficient (β), and the third-order nonlinear optical susceptibility (χ(3)) of Giemsa dye were measured. The measurements reveal that both n2 and β are dependent on the dye concentration. The obtained results indicate that the Giemsa dye exhibits positive nonlinear saturable absorption (SA) and negative refraction nonlinearity, manifestation of self-defocusing effect. Optical power limiting characteristics of the Giemsa dye at different concentrations in solution and polymer film were studied. The observed large third-order optical nonlinearity of Giemsa dye confirms that Giemsa dye is a promising nonlinear material for the optical power limiting and photonic devices applications.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Localized States in Discrete Nonlinear Schrödinger Equations
Cai, D; Grønbech-Jensen, N; Cai, David; Grønbech-Jensen, Niels
1993-01-01
A new 1-D discrete nonlinear Schrödinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The relationship between intrinsic localized states and the soliton of the Ablowitz-Ladik NLS is discussed. It is pointed out that a staggered localized state can be viewed as a particle of a {\\em negative} effective mass. It is shown that staggered localized states can exist in the discrete dark NLS. The motion of localized states and Peierls-Nabarro pinning are studied.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Zhao, Peng; Wang, Zonghua; Chen, Jishi; Zhou, Yu; Zhang, Fushi
2017-04-01
The nonlinear optical properties of the polymeric carboxyl phthalocyanine with lanthanum (LaPPc.COOH), holmium (HoPPc.COOH) and ytterbium (YbPPc.COOH) as centric atom, were investigated by the Z-scan method using a picosecond 532 nm laser. The synthesized phthalocyanines had steric polymeric structure and dissolved well in aqueous solution. The nonlinear optical response of them was attributed to the reverse saturable absorption and self-focus refraction. The nonlinear absorption properties decreased with the centric atoms changing from La, Ho to Yb. The largest second-order hyperpolarizability and optical limiting response threshold of LaPPc.COOH were 3.89 × 10-29 esu and 0.32 J/cm2, respectively. The reverse saturable absorption was explained by a three level mode of singlet excited state under the picosecond irradiation. The result indicates the steric structure presented additive stability of these polymeric phthalocyanines for their application as potential optical limiting materials.
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
A General Nonlinear Optimization Algorithm for Lower Bound Limit Analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...
Valligatla, Sreeramulu; Haldar, Krishna Kanta; Patra, Amitava; Desai, Narayana Rao
2016-10-01
The semiconductor nanocrystals are found to be promising class of third order nonlinear optical materials because of quantum confinement effects. Here, we highlight the nonlinear optical switching and optical limiting of cadmium selenide (CdSe) quantum dots (QDs) using nanosecond Z-scan measurement. The intensity dependent nonlinear absorption and nonlinear refraction of CdSe QDs were investigated by applying the Z-scan technique with 532 nm, nanosecond laser pulses. At lower intensities, the nonlinear process is dominated by saturable absorption (SA) and it is changed to reverse saturable absorption (RSA) at higher intensities. The SA behaviour is attributed to the ground state bleaching and the RSA is ascribed to free carrier absorption (FCA) of CdSe QDs. The nonlinear optical switching behaviour and reverse saturable absorption makes CdSe QDs are good candidate for all-optical device and optical limiting applications.
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Limits of localized control in extended nonlinear systems
Handel, Andreas
We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under
Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models
Institute of Scientific and Technical Information of China (English)
Jochen Aβfalg; Frank Allg(o)wer
2007-01-01
This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].
An Improved Lower Bound Limit State Optimisation Algorithm
DEFF Research Database (Denmark)
Frier, Christian; Damkilde, Lars
2010-01-01
Limit State analysis has been used in engineering practice for many years e.g. the yield-line method for concrete slabs and slip-line solutions in geotechnics. In the recent years there has been an increased interest in numerical Limit State analysis, and today algorithms take into account the non......-linear yield criteria. The aim of the paper is to refine an earlier presented effective method which reduces the number of optimisation variables considerably by eliminating the equilibrium equations a priori and improvements are made on the interior point optimisation algorithm....
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
State dependent matrices and balanced energy functions for nonlinear systems
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
The nonlinear extension of the balancing procedure requires the case of state dependent quadratic forms for the energy functions, i.e., the nonlinear extensions of the linear Gramians are state dependent matrices. These extensions have some interesting ambiguities that do not occur in the linear cas
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, Ron; Cross, M. C.; Roukes, M. L.
2013-01-01
In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator’s anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nano-electromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator’s phase noise, as predicted by our model. PMID:23679770
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
KUANG Mai-Hua; MA Shan-Jun; LIU Dong-Mei
2008-01-01
Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ>λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Superposition of nonlinear coherent states on a sphere
Directory of Open Access Journals (Sweden)
T Hosseinzadeh
2013-09-01
Full Text Available In this paper, by using the nonlinear coherent states on a sphere, we introduce superposition of the aforementioned coherent states. Then, we consider quantum optical properties of these new superposed states and compare these properties with the corresponding properties of the nonlinear coherent states on the sphere. Specifically, we investigate their characteristics function, photon-number distribution, Mandel parameter, quadrature squeezing, anti-bunching effect and Wigner function, and obtain the curvature effect on the properties of the superposed states. Finally, by using the trapped atom system, we introduce a theoretical scheme to generate superposition of the coherent states on the sphere.
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Kuzyk, Mark G
2014-01-01
The Thomas Kuhn Reich sum rules and the sum-over-states (SOS) expression for the hyperpolarizabilities are truncated when calculating the fundamental limits of nonlinear susceptibilities. Truncation of the SOS expression can lead to an accurate approximation of the first and second hyperpolarizabilities due to energy denominators, which can make the truncated series converge to within 10% of the full series after only a few excited states are included in the sum. The terms in the sum rule series, however, are weighted by the state energies, so convergence of the series requires that the position matrix elements scale at most in inverse proportion to the square root of the energy. Even if the convergence condition is met, serious pathologies arise, including self inconsistent sum rules and equations that contradict reality. As a result, using the truncated sum rules alone leads to pathologies that make any rigorous calculations impossible, let alone yielding even good approximations. This paper discusses condi...
Limit cycle analysis of active disturbance rejection control system with two nonlinearities.
Wu, Dan; Chen, Ken
2014-07-01
Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
Functional State Modelling of Cultivation Processes: Dissolved Oxygen Limitation State
Directory of Open Access Journals (Sweden)
Olympia Roeva
2015-04-01
Full Text Available A new functional state, namely dissolved oxygen limitation state for both bacteria Escherichia coli and yeast Saccharomyces cerevisiae fed-batch cultivation processes is presented in this study. Functional state modelling approach is applied to cultivation processes in order to overcome the main disadvantages of using global process model, namely complex model structure and a big number of model parameters. Alongwith the newly introduced dissolved oxygen limitation state, second acetate production state and first acetate production state are recognized during the fed-batch cultivation of E. coli, while mixed oxidative state and first ethanol production state are recognized during the fed-batch cultivation of S. cerevisiae. For all mentioned above functional states both structural and parameter identification is here performed based on experimental data of E. coli and S. cerevisiae fed-batch cultivations.
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi......-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better than estimators based on Taylor approximations. Nevertheless, the implementation is significantly simpler as no derivatives are required. Thus, it is believed that the new state estimators can replace well...
Origin of Soft Limits from Nonlinear Supersymmetry in Volkov--Akulov Theory
Kallosh, Renata; Murli, and Divyanshu
2016-01-01
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov--Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
On a state space approach to nonlinear H∞ control
Schaft, van der A.J.
1991-01-01
We study the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H∞ norm for the syste
Nonlinear H-ininity state feedback controllers:
DEFF Research Database (Denmark)
Cromme, Marc; Møller-Pedersen, Jens; Pagh Petersen, Martin
1997-01-01
From a general point of view the state feedback H∞ suboptimal control problem is reasonably well understood. Important problems remain with regard to a priori information of the size of the neighbourhood where the local state feedback H∞ problem is solvable. This problem is solved regionally (sem...
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Pérez-Moreno, Javier; Clays, Koen
The generalized Thomas-Kuhn sum rules are used to characterize the nonlinear optical response of organic chromophores in terms of fundamental parameters that can be measured experimentally. The nonlinear optical performance of organic molecules is evaluated from the combination of hyper-Rayleigh scattering measurements and the analysis in terms of the fundamental limits. Different strategies for the enhancement of nonlinear optical behavior at the molecular and supramolecular level are evaluated and new paradigms for the design of more efficient nonlinear optical molecules are proposed and investigated.
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Bartolini, R.
2016-01-01
This paper introduces the most recent achievements in the control of nonlinear dynamics in electron synchrotron light sources, with special attention to diffraction limited storage rings. Guidelines for the design and optimization of the magnetic lattice are reviewed and discussed.
Understanding of flux-limited behaviors of heat transport in nonlinear regime
Energy Technology Data Exchange (ETDEWEB)
Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)
2016-01-28
The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.
A nonlinear state-space approach to hysteresis identification
Noël, J. P.; Esfahani, A. F.; Kerschen, G.; Schoukens, J.
2017-02-01
Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.
LimitS - A system for limit state analysis and optimal material layout
DEFF Research Database (Denmark)
Damkilde, Lars; Krenk, Steen
1997-01-01
A system LimitS for limit state analysis and material optimization has been developed and implemented in a PC environment. The program is formulated in a general finite element format with stress-based elements. The solution method is based on the lower-bound theorem, where an optimal stress...... the statics and kinematics of the collapse mode are determined via the dual variables of the LP-problem. In LimitS the following element types are implemented: two- and three-dimensional beam elements; truss elements; triangular slab elements; and shear and stringer elements for plates with in-plane loading....... Examples of all three problem types are given including both limit state analysis and material optimization....
LimitS - A system for limit state analysis and optimal material layout
DEFF Research Database (Denmark)
Damkilde, Lars; Krenk, Steen
1997-01-01
A system LimitS for limit state analysis and material optimization has been developed and implemented in a PC environment. The program is formulated in a general finite element format with stress-based elements. The solution method is based on the lower-bound theorem, where an optimal stress...... the statics and kinematics of the collapse mode are determined via the dual variables of the LP-problem. In LimitS the following element types are implemented: two- and three-dimensional beam elements; truss elements; triangular slab elements; and shear and stringer elements for plates with in-plane loading....... Examples of all three problem types are given including both limit state analysis and material optimization....
Azulenic Chromophores For Optical Limiting and Other Nonlinear Optical Applications
2007-11-02
that azulene-containing polyenal analogs of retinal could be incorporated into the important retinal-protein, bacteriorhodopsin. The resulting...S. H. Liu, “Effects of Fluoro-Substituents on Excited State Properties of Conjugated Polyenes (Fluorinated Retinoids),” The Spectrum, 14, 8-12 (2002...Colmenares, A. E. Asato, and R. S. H. Liu, “Effects of Fluoro-Substituents on Excited State Properties of Conjugated Polyenes (Fluorinated Retinoids),” The
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
The light filament as a new nonlinear polarization state
Kovachev, Lubomir M
2015-01-01
We present an analytical approach to the theory of nonlinear propagation in gases of femtosecond optical pulses with broad-band spectrum . The vector character of the nonlinear third-order polarization of the electrical field in air is investigated in details. A new polarization state is presented by using left-hand and right-hand circular components of the electrical field . The corresponding system of vector amplitude equations is derived in the rotating basis. We found that this system of nonlinear equations has $3D+1$ vector soliton solutions with Lorentz shape. The solution presents a relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in a plane orthogonal to the direction of propagation. The evolution of the intensity profile demonstrates a weak self-compression and a week spherical wave in the first milliseconds of propagation.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet the implemen......In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...... the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace well-known filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state...
RELIABILITY ANALYSIS FOR IMPLICIT LIMIT STATE EQUATION
Institute of Scientific and Technical Information of China (English)
WANG Yan-ping; L(U) Zhen-zhou; YUE Zhu-feng
2005-01-01
In order to obtain the failure probability of the implicit limit state equation accurately, advanced mean value second order (AMVSO) method was presented, and advanced mean value (AMV) in conjunction with the response surface method (RSM)was also presented. The implementations were constructed on the basis of the advanced mean value first order (AMVFO) method and the RSM. The examples show that the accuracy of the AMVSO is higher than that of the AMVFO. The results of the AMV in conjunction with the RSM are not sensitive to the positions of the sampling points for determining the response surface equation, which illustrates the robustness of the presented method.
Nonlinear optical properties and optical limiting measurements of graphene oxide - Ag@TiO2 compounds
Ebrahimi, M.; Zakery, A.; Karimipour, M.; Molaei, M.
2016-07-01
In this work Graphene Oxide (GO), Ag@TiO2 core-shells and GO-Ag@TiO2 compounds were prepared and experimentally verified. Using a low power laser diode with 532 nm wavelength, the magnitude and the sign of the nonlinear refractive index and nonlinear absorption were determined by the Z-scan technique. It was observed that the nonlinear absorption of GO-Ag@TiO2 mixture was higher than pure GO. The optical limiting effect of these samples was also investigated using the 2nd harmonics of a pulsed Nd-YAG laser at 532 nm. Our results showed that the sole Ag@TiO2 didn't show any appreciable optical limiting effect, however after just mixing with graphene oxide the threshold of optical limiting was increased and the compound showed an enhancement of optical limiting behavior compared to GO itself. The presented results are discussed and compared with other literature reports.
Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber
Habib, G.; Kerschen, G.
2015-01-01
The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. PMID:27547085
Nonlinear platoon control of Arduino cars with range-limited sensors
Yue, Wei; Guo, Ge; Wang, Liyuan; Wang, Wei
2015-05-01
This paper investigates the problem of platoon control with sensor range limitation. A nonlinear vehicular platoon model is established, in which the sensing range constraint described by a piecewise nonlinear function is involved. Then a robust nonlinear control design method is proposed based on a disturbance observer and the backstepping technique. The results are obtained in the context of both individual vehicle stability and platoon string stability analysis, which can lead to substantially enhanced platoon control performance with a guaranteed level of attenuation of the disturbance caused by lead vehicle acceleration and wind gust. The effectiveness of the method has been shown by numerical simulations and experiments carried out with Arduino cars.
Hybrid Nonlinear Optical Materials for Applications in Power Limiting and Photorefractive Devices
2010-03-01
Final 3. DATES COVERED (From - To) 04/01/2007 to 11/30/2009 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER FA9550-07-1-0307 Hybrid Nonlinear Optical Materials for...Hybrid Nonlinear Optical Materials for Applications in Power Limiting and Photorefractive devices Prime Contract: FA95500710307
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Bankole, Owolabi M.; Nyokong, Tebello
2017-05-01
We report on the conjugation of azide-derivatized gold nanoparticles (AuNPs) to alkyne moieties of ZnPc and InPc via azide-alkyne Huisgen cycloaddition reaction to form phthalocyanines-AuNPs (MPc-AuNPs) conjugates. The detailed structural characterizations of the composites were in good agreement with the expected results. The nonlinear absorption coefficients and other nonlinear optical limiting parameters were almost two times larger for the conjugates compared to free phthalocyanines. We established direct relationship between improved photophysical characterizations and enhanced nonlinear effects of reverse saturable absorption mechanisms favoured by excited triplet absorption of the phthalocyanines in the presence of AuNPs. The combination of InPc with AuNPs resulted in the lowest limiting intensity value of 0.06 J/cm2, hence the best performance in terms of optical limiting.
On global attraction to stationary states for wave equations with concentrated nonlinearities
Kopylova, E.
2016-01-01
The global attraction to stationary states is established for solutions to 3D wave equations with concentrated nonlinearities: each finite energy solution converges as $t\\to\\pm\\infty$ to stationary states. The attraction is caused by nonlinear energy radiation.
Nonlinear Optical Spectroscopy of Excited States in Polyfluorene
Tong, M; Vardeny, Z V
2006-01-01
We used a variety of nonlinear optical (NLO) spectroscopies to study the singlet excited states order, and primary photoexcitations in polyfluorene; an important blue emitting p-conjugated polymer. The polarized NLO spectroscopies include ultrafast pump-probe photomodulation, two-photon absorption, and electroabsorption. For completeness we also measured the linear absorption and photoluminescence spectra. We found that the primary photoexcitations in polyfluorene are singlet excitons.
Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems
Directory of Open Access Journals (Sweden)
Hailiang Li
2003-09-01
Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.
Development of a wrinkled pipeline fatigue ultimate limit state criterion
Energy Technology Data Exchange (ETDEWEB)
Semiga, V.; Tiku, S.; Dinovitzer, A. [BMT Fleet Technology Ltd., Kanata (Canada); Zhou, J.; Sen, M. [TransCanada PipeLines Ltd., Calgary, AB (Canada)
2009-07-01
This paper described research currently being conducted to develop a mechanics-based wrinkle ultimate limit state for evaluating the long-term integrity of wrinkled pipeline segments. Efforts included testing and non-linear finite element analysis (FEA) of small-scale and full-scale wrinkled pipeline segments. The aim of the program was to develop a set of monotonic and cyclic material properties for use in designing a failure assessment procedure. A failure criterion has also been developed to predict the fatigue life of experimental pipeline specimens. An experimental material properties database was developed for several pipeline materials ranging from API grade X60 to X100 steel pipelines. Multiple monotonic tensile tests were conducted for all materials used in the program. Experimental stress-strain curves were used to develop finite element material models during the modelling phase of the project. Complete strain life curves were also obtained. A small scale strip test was developed to predict the fatigue life of strip test specimens. Nonlinear kinematic material models were also developed. Results of the program to date indicate that the finite element method (FEM) model is capable of accurately estimating the cyclic fatigue life of pipelines with wrinkles. It was concluded that the FEM model will also be used to examine the interactions between soil and buried pipelines. 6 refs., 14 figs.
Directory of Open Access Journals (Sweden)
Geoff Boeing
2016-11-01
Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.
Pan, Shuokai; Elliott, Stephen J; Teal, Paul D; Lineton, Ben
2015-06-01
Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementation of the saturating nonlinearity, the computational speed of this modified state space method is more than 40 times faster than that of the original formulation.
New theoretical framework for OFDM/CDMA systems with peak-limited nonlinearities
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new theoretical framework for the evaluation of the in-band nonlinear distortion effects on the performance of OFDM systems is presented. In contrast to previous works that approximate the nonlinear noise as a Gaussian additive random process, the new framework is based on the properties of the large deviations of a stationary Gaussian process and shot noise theories, which can evaluate the performance of the OFDM system with high accuracy, especially at realistic scenarios where the Gaussian approximation of the nonlinear noise is no longer valid. The approach can be used to evaluate many communication systems with peak-limited nonlinearities and high PAPR, such as the downlink performance analysis of large capacity DS-CDMA systems.
Application of nonlinear ultrasonic method for monitoring of stress state in concrete
Energy Technology Data Exchange (ETDEWEB)
Kim, Gyu Jin; Kwak, Hyo Gyoung [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Park, Sun Jong [Dept. of Structural System and Site Safety Evaluation, Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2016-04-15
As the lifespan of concrete structures increases, their load carrying capacity decreases owing to cyclic loads and long-term effects such as creep and shrinkage. For these reasons, there is a necessity for stress state monitoring of concrete members. Particularly, it is necessary to evaluate the concrete structures for behavioral changes by using a technique that can overcome the measuring limitations of usual ultrasonic nondestructive evaluation methods. This paper proposes the use of a nonlinear ultrasonic method, namely, nonlinear resonant ultrasonic spectroscopy (NRUS) for the measurement of nonlinearity parameters for stress monitoring. An experiment compared the use of NRUS method and a linear ultrasonic method, namely, ultrasonic pulse velocity (UPV) to study the effects of continuously increasing loads and cyclic loads on the nonlinearity parameter. Both NRUS and UPV methods found a similar direct relationship between load level and that parameter. The NRUS method showed a higher sensitivity to micro-structural changes of concrete than UPV method. Thus, the experiment confirms the possibility of using the nonlinear ultrasonic method for stress state monitoring of concrete members.
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Directory of Open Access Journals (Sweden)
Anju K. Augustine
2014-01-01
Full Text Available We present third-order optical nonlinear absorption in CdSe quantum dots (QDs with particle sizes in the range of 4.16–5.25 nm which has been evaluated by the Z-scan technique. At an excitation irradiance of 0.54 GW/cm2 the CdSe QDs exhibit reverse saturation indicating a clear nonlinear behavior. Nonlinearity increases with particle size in CdSe QDs within the range of our investigations which in turn depends on the optical band gap. The optical limiting threshold of the QDs varies from 0.35 GW/cm2 to 0.57 GW/cm2 which makes CdSe QDs a promising candidate for reverse-saturable absorption based devices at high laser intensities such as optical limiters.
Van Aert, S; Chen, J H; Van Dyck, D
2010-10-01
A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
Rips, Simon; Wilson-Rae, Ignacio; Hartmann, Michael J
2011-01-01
We propose a scheme to prepare nanomechanical oscillators in non-classical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonant frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables preparation of the nanomechanical oscillator in a single phonon Fock state. Our scheme can for example be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system
DEFF Research Database (Denmark)
Brøns, Morten; Sturis, Jeppe
2001-01-01
A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong...
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
Xie, Lihan; Baguet, Sébastien; Prabel, Benoit; Dufour, Régis
2016-01-01
International audience; A frequency-domain approach for direct parametric analysis of limit points of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of limit points is performed. The whole numerical procedure is based on the Harmonic Balance Method and can be decomposed in three distinct steps. Firstly, a response curve is calculated by HBM combined with a continuation technique ...
Nonlinear system identification and control using state transition algorithm
Yang, Chunhua; Gui, Weihua
2012-01-01
This paper presents a novel optimization method named state transition algorithm (STA) to solve the problem of identification and control for nonlinear system. In the proposed algorithm, a solution to optimization problem is considered as a state, and the updating of a solution equates to the process of state transition, which makes the STA easy to understand and convenient to be implemented. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results demonstrate the validity of the methodology, and comparison to STA with other optimization algorithms confirms that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence speed and more stable performance.
Progressive Bayes: a new framework for nonlinear state estimation
Hanebeck, Uwe D.; Briechle, Kai; Rauh, Andreas
2003-04-01
This paper is concerned with recursively estimating the internal state of a nonlinear dynamic system by processing noisy measurements and the known system input. In the case of continuous states, an exact analytic representation of the probability density characterizing the estimate is generally too complex for recursive estimation or even impossible to obtain. Hence, it is replaced by a convenient type of approximate density characterized by a finite set of parameters. Of course, parameters are desired that systematically minimize a given measure of deviation between the (often unknown) exact density and its approximation, which in general leads to a complicated optimization problem. Here, a new framework for state estimation based on progressive processing is proposed. Rather than trying to solve the original problem, it is exactly converted into a corresponding system of explicit ordinary first-order differential equations. Solving this system over a finite "time" interval yields the desired optimal density parameters.
Amigó, José M; Hirata, Yoshito; Aihara, Kazuyuki
2017-08-01
In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.
Amigó, José M.; Hirata, Yoshito; Aihara, Kazuyuki
2017-08-01
In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.
Application of nonlinear compensation to limit input dynamic range in analog optical fiber links
Directory of Open Access Journals (Sweden)
R. Garduno
2010-08-01
Full Text Available The dynamic range of a signal at the input of a measurement system during a short circuit test is increased severaltimes by the nominal input voltage. Saturation of the measurement system may occur in a device under failure test.This paper introduces the application of a nonlinear compensation to limit the voltage range at the input of a voltagecontrolled oscillator which is used to produce the pulsed frequency modulation needed to transmit the analog signalsover the optical fiber links. The proposed dynamic range compensation system is based on non-linear circuits toaccommodate the input range of the voltage controlled oscillator. This approach increases the transient signalhandling capabilities of the measuring system. This work demonstrates that the nonlinear compensated optical fiberapproach yields a unique, electrically isolated, lightning-proof analog data transmission system for remote measuringsystems in the highly aggressive EMI environment of high-power test laboratories.
Measurement-Induced Strong Kerr Nonlinearity for Weak Quantum States of Light
Costanzo, Luca S.; Coelho, Antonio S.; Biagi, Nicola; Fiurášek, Jaromír; Bellini, Marco; Zavatta, Alessandro
2017-07-01
Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the single photon level. We probe the induced nonlinearity with weak coherent states and characterize the output non-Gaussian states with quantum state tomography. The strong nonlinearity is clearly witnessed as a change of sign of specific off-diagonal density matrix elements in the Fock basis.
The de Sitter limit of inflation and non-linear perturbation theory
DEFF Research Database (Denmark)
Jarnhus, Philip; Sloth, Martin Snoager
2008-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug......, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function....
The de Sitter limit of inflation and non-linear perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jarnhus, Philip R; Sloth, Martin S, E-mail: pjarn@phys.au.dk, E-mail: sloth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2008-02-15
We study the fourth-order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in non-linear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the nth-order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
Identification of a Class of Non-linear State Space Models using RPE Techniques
DEFF Research Database (Denmark)
Zhou, Wei-Wu; Blanke, Mogens
1989-01-01
The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...
State estimation of connected vehicles using a nonlinear ensemble filter
Institute of Scientific and Technical Information of China (English)
刘江; 陈华展; 蔡伯根; 王剑
2015-01-01
The concept of connected vehicles is with great potentials for enhancing the road transportation systems in the future. To support the functions and applications under the connected vehicles frame, the estimation of dynamic states of the vehicles under the cooperative environments is a fundamental issue. By integrating multiple sensors, localization modules in OBUs (on-board units) require effective estimation solutions to cope with various operation conditions. Based on the filtering estimation framework for sensor fusion, an ensemble Kalman filter (EnKF) is introduced to estimate the vehicle’s state with observations from navigation satellites and neighborhood vehicles, and the original EnKF solution is improved by using the cubature transformation to fulfill the requirements of the nonlinearity approximation capability, where the conventional ensemble analysis operation in EnKF is modified to enhance the estimation performance without increasing the computational burden significantly. Simulation results from a nonlinear case and the cooperative vehicle localization scenario illustrate the capability of the proposed filter, which is crucial to realize the active safety of connected vehicles in future intelligent transportation.
Nonlinear Filtering Techniques Comparison for Battery State Estimation
Directory of Open Access Journals (Sweden)
Aspasia Papazoglou
2014-09-01
Full Text Available The performance of estimation algorithms is vital for the correct functioning of batteries in electric vehicles, as poor estimates will inevitably jeopardize the operations that rely on un-measurable quantities, such as State of Charge and State of Health. This paper compares the performance of three nonlinear estimation algorithms: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter, where a lithium-ion cell model is considered. The effectiveness of these algorithms is measured by their ability to produce accurate estimates against their computational complexity in terms of number of operations and execution time required. The trade-offs between estimators' performance and their computational complexity are analyzed.
Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators
Natalie Ramos Pedroza; William MacKunis; Golubev, Vladimir V.
2014-01-01
In this paper, a synthetic jet actuators (SJA)-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO) in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicat...
Ultimate Limit State Model Basis for Assessment of Offshore Wind Energy Converters
DEFF Research Database (Denmark)
Thöns, Sebastian; Faber, M. H.; Rücker, W.
2012-01-01
structure and the tripod structure are determined with a geometrically and materially nonlinear finite element analysis. The observed failure mechanisms are the basis for the definition of the ultimate limit state responses. A probabilistic model accounting for the uncertainties involved is derived...... on the basis of literature review and measurement data from a prototype Multibrid M5000 support structure. In combination with the developed structural and loading models, sensitivity analyses in regard to the responses are peiformed to enhance the understanding and to refine the developed models. To this end...... variables on the responses including nonlinearity the refinement of the model is performed on a quantitative basis....
Linear and Nonlinear Analysis of Magnetic Bearing Bandwidth Due to Eddy Current Limitations
Kenny, Andrew; Palazzolo, Alan
2000-01-01
Finite element analysis was used to study the bandwidth of alloy hyperco50a and silicon iron laminated rotors and stators in magnetic bearings. A three dimensional model was made of a heteropolar bearing in which all the flux circulated in the plane of the rotor and stator laminate. A three dimensional model of a plate similar to the region of a pole near the gap was also studied with a very fine mesh. Nonlinear time transient solutions for the net flux carried by the plate were compared to steady state time harmonic solutions. Both linear and quasi-nonlinear steady state time harmonic solutions were calculated and compared. The finite element solutions for power loss and flux bandwidth were compared to those determined from classical analytical solutions to Maxwell's equations.
Saravanan, M.; T. C., Sabari Girisun
2017-01-01
Nonlinear absorption and optical limiting properties of ZnFe2O4-rGO magnetic nanostructures was investigated by the Z-scan technique using Q-switched Nd:YAG laser (5 ns, 532 nm, 10 Hz) as an excitation source. Excited state absorption was the dominant process responsible for the observed nonlinearity in ZnFe2O4 decorated rGO which arises due to photo-generated charge carriers in the conduction band of zinc ferrite and increases in defects at the surface of rGO due to the incorporation of ZnFe2O4. The magnitude of the nonlinear absorption co-efficient was found to be in the order of 10-10 m/W. A noteworthy enhancement in the third-order NLO properties in ZnFe2O4-(15 wt%) rGO with those of individual counter parts and well known graphene composites was reported. Role of induced defects states (sp3) arising from the functionalization of rGO in the enhancement of NLO response was explained through Raman studies. Earlier incorporation and distribution of ZnFe2O4 upon GO through one-step hydrothermal method was analyzed by XRD and FTIR. Formation of (nanospheres/nanospindles) ZnFe2O4 along with reduction of graphene oxide was confirmed through TEM analysis. VSM studies showed zinc ferrite decorated rGO posseses superparamagnetic behavior. The tuning of nonlinear optical and magnetic behavior with variation in the content of spinel ferrites upon reduced graphene oxide provides an easy way to attain tunable properties which are exceedingly required in both optoelectronics and photothermal therapy applications.
Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
Chen, Shouxin; Yang, Yisong
2015-01-01
This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics ...
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Charged anisotropic matter with linear or nonlinear equation of state
Varela, Victor; Ray, Saibal; Chakraborty, Kaushik; Kalam, Mehedi
2010-01-01
Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplification achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or non-linear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the...
Three-state interactions determine the second-order nonlinear optical response
Perez-Moreno, Javier
2016-01-01
Using the sum-rules, the sum-over-states expression for the diagonal term of first hyperpolarizability can be expressed as the sum of three-state interaction terms. We study the behavior of a generic three-state term to show that is possible to tune the contribution of resonant terms by tuning the spectrum of the molecule. When extrapolated to the off-resonance regime, the three-state interaction terms are shown to behave in a similar manner as the three-level model used to derive the fundamental limits. We finally show that most results derived using the three-level ansatz are general, and apply to molecules where more than three levels contribute to the second-order nonlinear response or/and far from optimization.
Liquid-state acoustically-nonlinear nanoplasmonic source of optical frequency combs
Maksymov, Ivan S
2016-01-01
Nonlinear acoustic interactions in liquids are effectively stronger than nonlinear optical interactions in solids. Thus, harnessing these interactions will offer new possibilities in the design of ultra-compact nonlinear photonic devices. We theoretically demonstrate a hybrid, liquid-state and nanoplasmonic, source of optical frequency combs compatible with fibre-optic technology. This source relies on a nanoantenna to harness the strength of nonlinear acoustic effects and synthesise optical spectra from ultrasound.
Directory of Open Access Journals (Sweden)
Xia Liu
2017-02-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.
A general non-linear optimization algorithm for lower bound limit analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....
Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series.
Gao, Zhong-Ke; Cai, Qing; Yang, Yu-Xuan; Dang, Wei-Dong; Zhang, Shan-Shan
2016-10-19
Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.
Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series
Gao, Zhong-Ke; Cai, Qing; Yang, Yu-Xuan; Dang, Wei-Dong; Zhang, Shan-Shan
2016-10-01
Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.
Kamath, Laxminarayana; Manjunatha, K. B.; Shettigar, Seetharam; Umesh, G.; Narayana, B.; Samshuddin, S.; Sarojini, B. K.
2014-03-01
A series of new chalcones containing terphenyl as a core and with different functional groups has been successfully synthesized by Claisen-Schmidt condensation method in search of new nonlinear optical (NLO) materials. Molecular structural characterization for the compounds was achieved by FTIR and single crystal X-ray diffraction. The third-order NLO absorption and refraction coefficients were simultaneously determined by Z-scan technique. The measurements were performed at 532 nm with 7 ns laser pulses using a Nd:YAG laser in solution form. The Z-scan experiments reveal that the compounds exhibit strong nonlinear refraction coefficient of the order 10-11 esu and the molecular two photon absorption cross section is 10-46 cm4 s/photon. The results also show that the structures of the compounds have great impact on NLO properties. The compounds show optical power limiting behavior due to two-photon absorption (TPA).
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), E. T. S. I. Industriales, Avda. Camilo Jose Cela, s/n Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain)
2009-01-23
We introduce a model of a Bose-Einstein condensate based on the one-dimensional nonlinear Schroedinger equation, in which the nonlinear term depends on the domain. The nonlinear term changes a cubic term into a quintic term, according to the domain considered. We study the existence, stability and bifurcation of solutions, and use the qualitative theory of dynamical systems to study certain properties of such solutions.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
Analysis of key properties for optical power limiting and the influence of nonlinear scattering
Koerber, M.; Azarian, A.; Schwarz, B.; Eberle, B.
2014-10-01
In this paper, we propose ways to study the optical limiting behavior of dissolved nanoparticles. We want to present two different approaches. First, we identify the key properties responsible for the critical fluence threshold using a principal component analysis. For metallic nanoparticles, we found that the real part of the complex dielectric function must have a negative value as low as possible, while the imaginary part must be close to zero. Additionally, the solvent should have a low refractive index as well as a low absorption. Furthermore, nonlinear scattering seems to be an important limiting mechanism for nanoparticle limiters. Here, we present a thermal finite element model to predict the temporal evolution of the temperature profile in the nanoparticles and their vicinity. The temperature profile leads to vapor bubbles around the nanoparticles and Mie theory is used to calculate the induced scattering. We demonstrate the functionality of the model by simulating an Au-nanoparticle in an ethanol solution.
Identification of a class of nonlinear state-space models using RPE techniques
DEFF Research Database (Denmark)
Zhou, W. W.; Blanke, Mogens
1986-01-01
The recursive prediction error methods in state-space form have been efficiently used as parameter identifiers for linear systems, and especially Ljung's innovations filter using a Newton search direction has proved to be quite ideal. In this paper, the RPE method in state-space form is developed...... to the nonlinear case and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows...... a quite convincing performance of the filter as combined parameter and state estimator....
Lin, Tai-Chia; Petrovic, Milan S; Hajaiej, Hichem; Chen, Goong
2016-01-01
The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schrodinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln\\Gamma$) of the lower bound of the ground state energy as the coefficient $\\Gamma$ of the nonlinear term tends to infinity.
Tereshchenko, S. A.; Savelyev, M. S.; Podgaetsky, V. M.; Gerasimenko, A. Yu.; Selishchev, S. V.
2016-09-01
A threshold model is described which permits one to determine the properties of limiters for high-powered laser light. It takes into account the threshold characteristics of the nonlinear optical interaction between the laser beam and the limiter working material. The traditional non-threshold model is a particular case of the threshold model when the limiting threshold is zero. The nonlinear characteristics of carbon nanotubes in liquid and solid media are obtained from experimental Z-scan data. Specifically, the nonlinear threshold effect was observed for aqueous dispersions of nanotubes, but not for nanotubes in solid polymethylmethacrylate. The threshold model fits the experimental Z-scan data better than the non-threshold model. Output characteristics were obtained that integrally describe the nonlinear properties of the optical limiters.
Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth
Directory of Open Access Journals (Sweden)
Hua Jin
2017-03-01
Full Text Available This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial. We do not use the Ambrosetti-Rabinowitz condition, or the monotonicity condition on the nonlinearity.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
An Improved Lower Bound Limit State Optimisation Algorithm
DEFF Research Database (Denmark)
Frier, Christian; Damkilde, Lars
2010-01-01
Limit State analysis has been used in manual design methods for decades e.g. the yield line theory for concrete slabs.......Limit State analysis has been used in manual design methods for decades e.g. the yield line theory for concrete slabs....
Characterizaticr of Solid State Laser and Nonlinear Optical Materials.
1995-02-02
materials useful in the different methods for obtaining frequency agility: narrow line emitters with multiple lasing channels and nonlinear optical materials . In...codoped with two or more rare earth ions were studied and computers models developed to explain their spectral dynamics. The nonlinear optical materials investigated
Physics of the fundamental limits of nonlinear optics: a theoretical perspective [Invited
Lytel, Rick
2016-12-01
The theory of the fundamental limits (TFL) of nonlinear optics is a powerful tool for experimentalists seeking to create molecules and materials with large responses, and for theorists who are seeking to understand how the basic elements of quantum theory delineate the boundaries within which these searches should be conducted. On a practical level, the TFL provides a metric for measuring the performance or 'goodness' of new molecules, relative to what is possible. Explorations of large sets of structures within the theory provide insight into new design rules for creating more active molecules. This article is a review of the TFL, starting with a history of its development and its first use to discover that all molecules as of the year 2000 fell a factor of 30 below the limits, and continuing to the present day where the theory continues to provide research opportunities and challenges. The review focuses on off-resonant nonlinear optics in order to sharply focus on the key elements of the TFL, but pointers are provided to the literature for near- and on-resonance applications.
Physics of the fundamental limits of nonlinear optics: A theoretical perspective
Lytel, Rick
2016-01-01
The theory of the fundamental limits (TFL) of nonlinear optics is a powerful tool for experimentalists seeking to create molecules and materials with large responses, and for theorists who are seeking to understand how the basic elements of quantum theory delineate the boundaries within which these searches should be conducted. On a practical level, the TFL provides a metric for measuring the performance or 'goodness' of new molecules, relative to what is possible. Explorations of large sets of structures within the theory provide insight into new design rules for creating more active molecules. This article is a review of the TFL, starting with a history of its development and its first use to discover that all molecules as of the year 2000 fell a factor of 30 below the limits, and continuing to the present day where the theory continues to provide research opportunities and challenges. The review focuses on off-resonant nonlinear optics in order to sharply focus on the key elements of the TFL, but pointers ...
Nonlinear absorption and optical limiting in Duran glass induced by 800 nm femtosecond laser pulses
Energy Technology Data Exchange (ETDEWEB)
Jamshidi-Ghaleh, Kazem [Department of Physics, Azerbaijan University of Tarbiat Moallem, Tabriz (Iran, Islamic Republic of); Mansour, Nastaran [Department of Physics, Shahi Beheshti University, Tehran (Iran, Islamic Republic of)
2007-01-21
Nonlinear absorption of Duran glass by irradiation of a focused 200 fs pulsed laser were investigated using the z-scan technique at 800 nm. Optical limiting behaviour in this glass has also been measured. The limiting threshold was measured to 33 {mu}J pulse energy (peak intensity of 2.4 x 10{sup 12} W cm{sup -2}) in this sample. The decrease in transmitted intensity is around 75% compared with the theoretical linear transmission for incident pulses pulse energies 320 {mu}J (peak intensity of 5 x 10{sup 12} W cm{sup -2}). A comparison of the theoretical analyses with the experimental results shows that three-photon absorption and three-photon generated free-carrier absorption within the glasses are the main mechanisms for the observed nonlinear response. The values of the three-photon absorption coefficient and the photo-generated free-carrier cross section are measured as {gamma} = 2 x 10{sup -24}cm{sup 3} W{sup -2} and {sigma} = 1.2 x 10{sup -18} cm{sup 2}, respectively.
Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides.
Energy Technology Data Exchange (ETDEWEB)
Soh, Daniel Beom Soo
2017-09-01
We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2 ), particularly for those linear and nonlinear tran- sition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matri- ces that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibil- ities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators
Directory of Open Access Journals (Sweden)
Natalie Ramos Pedroza
2014-09-01
Full Text Available In this paper, a synthetic jet actuators (SJA-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicative parametric uncertainty in the actuator dynamic model. The result was achieved via innovative algebraic manipulation in the error system development, along with a Lyapunov-based robust control law. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic LCO suppression, considering a detailed dynamic model of the pitching and plunging dynamics. Numerical simulation results are provided to demonstrate the robustness and practical performance of the proposed control law.
Identification of Nonlinear Nonautonomous State Space Systems from Input-Output Measurements
Verdult, Vincent; Verhaegen, Michel; Scherpen, Jacquelien
2000-01-01
This paper presents a method to determine a nonlinear state space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
Deterministic superresolution with coherent states at the shot noise limit
DEFF Research Database (Denmark)
Distante, Emanuele; Jezek, Miroslav; Andersen, Ulrik L.
2013-01-01
detection approaches. Here we show that superresolving phase measurements at the shot noise limit can be achieved without resorting to nonclassical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection, and a deterministic......Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that superresolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multiparticle states of light or using complex...... binarization processing technique, we show a narrowing of the interference fringes that scales with 1/√N where N is the mean number of photons of the coherent state. Experimentally we demonstrate a 12-fold narrowing at the shot noise limit....
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
On the limits of probabilistic forecasting in nonlinear times series analysis
Amigó, José M.; Hirata, Yoshito; Aihara, Kazuyuki
2016-12-01
The ignorance score measures the quality of probabilistic forecasting. In this paper, we study its basic properties in the perfect model scenario, i.e., under the assumption that the system producing the data is perfectly known. Two further qualifications are added to this general setting. First, the system is a discrete-time, measure-preserving dynamical system. Moreover, randomness results from the quantization of the state space (i.e., from the finite precision of the observations), rather than being introduced via observational noise. In this "non-linear" perfect model scenario we derive, in particular, the admissible domain of the ignorance score and relate it with the ignorance score in imperfect models.
Limit state of structural elements during inelastic deformation
Nikitenko, A. F.; Reznikov, B. S.
2010-01-01
It is shown that, in the case of an axisymmetric stress state, the solution of the statically definable boundary-value problem for an ideal rigid-plastic body using the Mises-Schleicher strength criterion is extended to the rigid-creep model with any specified creep-rupture strength and corresponds to the limit state of a real creeping body.
Direct methods for limit states in structures and materials
Weichert, Dieter
2014-01-01
Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.
Enhancement of Kerr nonlinearity and its application to entangled state discrimination
Institute of Scientific and Technical Information of China (English)
NIU Yue-ping; QIAN Jun; FENG Xun-li; GONG Shang-qing
2007-01-01
In this paper, the recent research on the enhan-ced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously gen-erated coherence, are presented to enhance the Kerr nonlin-earity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr no-nlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Home-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method
Ewing, Craig Michael
1999-10-01
Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients. This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization. The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem. The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined. While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was
A bias identification and state estimation methodology for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
DEFF Research Database (Denmark)
Dollerup, Niels; Jepsen, Michael S.; Frier, Christian;
2014-01-01
A robust and effective finite element based implementation of lower bound limit state analysis applying an interior point formulation is presented in this paper. The lower bound formulation results in a convex optimization problem consisting of a number of linear constraints from the equilibrium...... equations and a number of convex non-linear constraints from the yield criteria. The computational robustness has been improved by eliminating a large number of the equilibrium equations a priori leaving only the statical redundant variables as free optimization variables. The elimination of equilibrium...... equations is based on a optimized numbering of elements and stress variables based on the frontal method approach used in the standard finite element method. The optimized numbering secures sparsity in the formulation. The convex non-linear yield criteria are treated directly in the interior point...
Tkachova, P.; Krot, A.; Minervina, H.
It is well known that there is chaos in convective process in atmosphere and ocean. In particular,dynamic model of Lorenz [1] describes the Rayleigh-Benard convection phenomenon. Phase trajectories of Lorenz equation system are characterized by strange alternative properties: on the one hand, they diverge (because of positive Lyapunov exponents), on the second hand, they attract to the limited domain of phase space called an attractor [1]. The Lorenz attractor has specific geometrical structure and can be characterized by means of fractal dimension. In this connection the aim of this work is development of analysis of Lorenz attractor based on the proposed nonlinear decomposition into matrix series [2]. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attractors and predict their evolution in time. Using results of matrix decomposition [2], it is not difficult to see that the change of vector function (describing the Lorenz attractor) can be approximated by only linear and quadratic terms [3]. Because values of the first and second order derivatives can be calculated by means of numerical methods we can estimate the change of the vector function from computational experiment. In result, the values of parameters of the Lorenz's attractor can be estimated. This permits us to solve the identification task of the current dynamical state of a convective aerodynamic flows. Moreover, using the results of matrix decomposition we can estimate the minimal embedding dimension [4] for the Lorenz attractor based on experimental data. References: [1] P.Berge,Y.Pomeau and C.Vidal. L'ordre dans le chaos: Vers une approche deterministe de la turbulence. Hermann:Paris,1988. [2] A.M.Krot, "Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system", Nonlinear Phenomena in Complex Systems,vol.4, N2, pp.106- 115, 2001. [3] A.M.Krot and P
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
2017-03-01
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
MCMC for non-linear state space models using ensembles of latent sequences
2013-01-01
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble ...
State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
Nonlinear absorption of SWNT film and its effects to the operation state of pulsed fiber laser.
Li, Xiaohui; Wang, Yonggang; Wang, Yishan; Zhao, Wei; Yu, Xuechao; Sun, Zhipei; Cheng, Xueping; Yu, Xia; Zhang, Ying; Wang, Qi Jie
2014-07-14
We study a single-wall carbon nanotube (SWNT) Polyvinyl alcohol (PVA) composite as a saturable absorber (SA) for pulse generation in Yb-doped fiber lasers. The saturable absorption and optical limiting (OL) characteristics of the SWNT device are investigated. By combing these two nonlinear effects, we find out for the first time, to the best of our knowledge, that mode-locking can be obtained in the dissipative soliton regime at low pumping followed by Q-switching at high pumping, which is quite different from conventional pulse dynamic evolutions. The Q-switched state operating at higher pump powers is due to the OL effect. The inverted operating fiber laser can be applied in various potential applications such as versatile material processing, optical communication and radar system etc.
Ultrafast and nonlinear optical characterization of optical limiting processes in fullerenes
Energy Technology Data Exchange (ETDEWEB)
Kohlman, R.; Klimov, V.; Shi, X. [and others
1997-10-01
The authors present recent results of broadband femotosecond (fs) transient absorption (TA) and broadband nanosecond (ns) optical limiting (OL) studies of C{sub 60} and derivatized C{sub 60}. Improvements in measurement techniques for fs TA spectra provide sensitivity to 10{sup {minus}5} in differential transmission, allowing detailed comparison of excited-state spectra with established energy level diagrams, as well as comparison of the ratio of triplet to singlet excited-state absorption cross sections from TA spectra with those obtained by modeling time transients at different wavelengths. For derivatized fullerenes, which provide enhanced solubility and a ground-state absorption extended into the infrared compared with C{sub 60} there is no spectral region where the triplet absorption cross section dominates the singlet as strongly as demonstrating broadband limiting in all 6, 6 mono-adducts and neat C{sub 60}. The authors report new approaches to processing sol-gel encapsulated fullerenes to improve the OL performance of solid-state materials to approach the response of solution limiters.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.
2011-05-11
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Coherent States, Dynamics and Semiclassical Limit on Quantum Groups
Aref'eva, I Ya; Viswanathan, K S; Volovich, I V
1994-01-01
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.
Understanding children's and adults' limitations in mental state reasoning.
Birch, Susan A J; Bloom, Paul
2004-06-01
Young children exhibit several deficits in reasoning about their own and other people's mental states. We propose that these deficits, along with more subtle limitations in adults' social-cognitive reasoning, are all manifestations of the same cognitive bias. This is the 'curse of knowledge' - a tendency to be biased by one's own knowledge when attempting to appreciate a more naïve or uninformed perspective. We suggest the developmental differences in mental state reasoning exist because the strength of this bias diminishes with age, not because of a conceptual change in how young children understand mental states. By pointing out the common denominator in children's and adults' limitations in mental state reasoning we hope to provide a unified framework for understanding the nature and development of social cognition.
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
DEFF Research Database (Denmark)
Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.
2002-01-01
The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...
State Child Care Policies for Limited English Proficient Families
Firgens, Emily; Matthews, Hannah
2012-01-01
The Child Care and Development Block Grant (CCDBG), the largest source of federal funding for child care assistance available to states, provides low-income families with help paying for child care. Studies have shown that low-income LEP (limited English proficient), as well as immigrant families, are less likely to receive child care assistance.…
Quantum limits of Eisenstein series and scattering states
DEFF Research Database (Denmark)
Petridis, Y.N.; Raulf, N.; Risager, Morten S.
2013-01-01
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak. © Cana...
Erratum to "Quantum Limits of Eisenstein Series and Scattering States''
DEFF Research Database (Denmark)
Petridis, Y.N.; Raulf, N.; Risager, Morten S.
2013-01-01
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak. © Cana...
Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization
Energy Technology Data Exchange (ETDEWEB)
Li, Q.; Chen, W. [School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan Province (China); Wang, Y.; Jia, J. [School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue 639798, Singapore (Singapore); Han, M. [School of Engineering, Temasek Polytechnic, Tampines 529757, Singapore (Singapore)
2009-10-20
By utilizing the state feedback exact linearization approach, a nonlinear robust control strategy is designed based on a multiple-input multiple-output (MIMO) dynamic nonlinear model of proton exchange membrane fuel cell (PEMFC). The state feedback exact linearization approach can achieve the global exact linearization via the nonlinear coordinate transformation and the dynamic extension algorithm such that H{sub {infinity}} robust control strategy can be directly utilized to guarantee the robustness of the system. The proposed dynamic nonlinear model is tested by comparing the simulation results with the experimental data in Fuel Cell Application Centre in Temasek Polytechnic. The comprehensive results of simulation manifest that the dynamic nonlinear model with nonlinear robust control law has better transient and robust stability when the vehicle running process is simulated. The proposed nonlinear robust controller will be very useful to protect the membrane damage by keeping the pressure deviations as small as possible during large disturbances and prolong the stack life of PEMFC. (author)
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Dynamical disappearance of superposition states in the thermodynamic limit
Frasca, M
2003-01-01
It is shown that a macroscopic superposition state of radiation, strongly interacting with an ensemble of two-level atoms, is removed generating a coherent state describing a classical radiation field, when the thermodynamic limit is taken on the unitary evolution obtained by the Schroedinger equation. Decoherence appears as a dynamical effect in agreement with a recent proposal [M. Frasca, Phys. Lett. A 283, 271 (2001)]. To prove that this effect is quite general, we show that this same behavior appears when a superposition of two Fock number states is also considered. Higher order corrections are computed showing that this result tends to become exact in the thermodynamic limit. It appears as a genuine example of intrinsic collapse of the wave function.
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...... are examined. The importance of the existence of stable immobile solitons in the two-dimensional dynamics of the travelling pulses is demonstrated. The process of forming narrow states from initially broad standing or moving excitations through the quasi-collapse mechanism is analyzed. The typical scenario...
Localized excitations in nonlinear complex systems current state of the art and future perspectives
Cuevas-Maraver, Jesús; Frantzeskakis, Dimitri; Karachalios, Nikos; Kevrekidis, Panayotis; Palmero-Acebedo, Faustino
2014-01-01
The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
Linear and nonlinear photonic Jackiw-Rebbi states in interfaced binary waveguide arrays
Tran, Truong X.; Biancalana, Fabio
2017-07-01
We study analytically and numerically the optical analog of the Jackiw-Rebbi states in quantum-field theory. These solutions exist at the interface of two binary waveguide arrays, which are described by two Dirac equations with masses of opposite sign. We show that these special states are topologically robust not only in the linear regime, but also in the nonlinear one (with both focusing and defocusing nonlinearities). We also reveal that one can effectively generate Jackiw-Rebbi states starting from Dirac solitons.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
LS-based discrete-time adaptive nonlinear control——Feasibility and limitations
Institute of Scientific and Technical Information of China (English)
郭雷; 魏晨Institute of Systems Science; Chinese Academy of Sciences; Beijing 100080; China
1996-01-01
Global stability and instability of a class of discrete-time adaptive nonlinear control systems are investigated.The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterizEd by a nonlinear function f(x).It is shown that in the scalar parameter case,when the standard least-squares (LS) method is used in estimation,the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| =0(||x||b) with b<8.Moreover,in the case where b≥8,it is also shown that the dosed-loop adaptive control system does not have global stability in general.Both the results found and the new analytical methods introduced may be regarded as a basic step for further study of discrete-time adaptive nonlinear control systems.
Institute of Scientific and Technical Information of China (English)
Jeffery C. DiFranco; Peter D. Miller; Benson K. Muite
2011-01-01
The purpose of this paper is to present a comparison between the modified nonlinear Schr(o)dinger (MNLS) equation and the focusing and defocusing variants of the (unmodified) nonlinear Schr(o)dinger (NLS) equation in the semiclassical limit.We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods.The main message is that,depending on initial data,the MNLS equation can behave either like the defocusing NLS equation,like the focusing NLS equation (in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data),or like an interesting mixture of the two.In the latter case,we identify a feature of the dynamics analogous to a sonic line in gas dynamics,a free boundary separating subsonic flow from supersonic flow.
Directory of Open Access Journals (Sweden)
Gang Chen
2012-01-01
Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.
Manjunatha, K. B.; Rajarao, Ravindra; Umesh, G.; Ramachandra Bhat, B.; Poornesh, P.
2017-08-01
A salen-based ruthenium (Ru) (II) complex was synthesized for possible use in nonlinear optical device applications. The Ru complex was doped in a polymer matrix to fabricate films using a low-cost spin-coating technique. The third-order nonlinear optical parameters of the complex were investigated by Z-scan and degenerate four-wave mixing techniques. The study reveals two-order enhancement of third-order optical susceptibility χ (3) and exhibits superior limiting capability due to a reverse saturable absorption process. All-optical switching action for the films indicates that the sample can function as an optical inverter or a NOT gate. Hence, the Ru (II) Schiff-base complex materializes as a possible candidate for use in nonlinear optical devices.
Analysis of steady-state and dynamical radially-symmetric problems of nonlinear viscoelasticity
Stepanov, Alexey B.
This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions. he treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total
Burst limit state reliability for fiber-wrapped steel pipe
Energy Technology Data Exchange (ETDEWEB)
Dann, Markus R. [University of Calgary (Canada); Maes, Marc A. [Blade Energy Partners Ltd. (Canada); Salama, Mamdouh M. [ConocoPhillips Company (United States)
2010-07-01
In the oil and gas sector, due to the increase in demand, pipeline projects are being developed in remote areas with harsh environments. High strength steel pipelines have been developed but due to their high cost and to low production capacity, the focus is now on dry fiber augmented steel technology pipelines (FAST-Pipe). The aim of this paper is to present a probabilistic mechanical burst limit state for such fiber wrapped pipelines. This model has been developed based on a large strain Cauchy stress formulation and has been used to perform a reliability comparison between an X80 pipe and an X70 FAST-Pipe. Results showed that the FAST-Pipe has more uncertainties than the high strength steel pipe and thus lower factors should be used in their design. This paper provided a probabilistic limit state model which can be used for both steel pipes and FAST-Pipe.
Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters
Sun, Tao; Xin, Ming
2017-05-01
Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.
Direct measurement of non-linear properties of bipartite quantum states
Bovino, F A; Castagnoli, G C; Ekert, A; Horodecki, P; Sergienko, A V; Alves, Carolina Moura; Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Pawel; Sergienko, Alexander Vladimir
2005-01-01
Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.
A nonlinear plasmonic resonator for three-state all-optical switching
Amin, Muhammad
2014-01-01
A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator\\'s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.
Spatially inhomogeneous electron state deep in the extreme quantum limit of strontium titanate.
Bhattacharya, Anand; Skinner, Brian; Khalsa, Guru; Suslov, Alexey V
2016-09-29
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate. Our experiments probe deeply into the regime where theory has long predicted an interaction-driven charge density wave or Wigner crystal state. A number of interesting features arise in the transport in this regime, including a striking re-entrant nonlinearity in the current-voltage characteristics. We discuss these features in the context of possible correlated electron states, and present an alternative picture based on magnetic-field induced puddling of electrons.
Fenili, André
2012-11-01
In this paper the author investigates the angular position and vibration control of a nonlinear rigid-flexible two link robotic manipulator considering fast angular maneuvers. The nonlinear control technique named State-Dependent Riccati Equation (SDRE) is used here to achieve these aims. In a more realistic approach, it is considered that some states can be measured and some states cannot be measured. The states not measured are estimated in order to be used for the SDRE control. These states are all the angular velocities and the velocity of deformation of the flexible link. A state-dependent Riccati equation-based estimator is used here. Not only different initial conditions between the system to be controlled (here named "real" system) and the estimator but also a different mathematical model is considered as the estimation model in order to verify the limitations of the proposed estimation and control techniques. The mathematical model that emulates the real system to be controlled considers two modes expansion and the estimation model considers only one mode expansion. The results for the different approaches are compared and discussed.
Duan, Zhaoxia; Xiang, Zhengrong; Karimi, Hamid Reza
2014-07-01
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality-based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Sun, Xiaodian; Jin, Li; Xiong, Momiao
2008-01-01
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.
Interface Limited Lithium Transport in Solid-State Batteries.
Santhanagopalan, Dhamodaran; Qian, Danna; McGilvray, Thomas; Wang, Ziying; Wang, Feng; Camino, Fernando; Graetz, Jason; Dudney, Nancy; Meng, Ying Shirley
2014-01-16
Understanding the role of interfaces is important for improving the performance of all-solid-state lithium ion batteries. To study these interfaces, we present a novel approach for fabrication of electrochemically active nanobatteries using focused ion beams and their characterization by analytical electron microscopy. Morphological changes by scanning transmission electron microscopy imaging and correlated elemental concentration changes by electron energy loss spectroscopy mapping are presented. We provide first evidence of lithium accumulation at the anode/current collector (Si/Cu) and cathode/electrolyte (LixCoO2/LiPON) interfaces, which can be accounted for the irreversible capacity losses. Interdiffusion of elements at the Si/LiPON interface was also witnessed with a distinct contrast layer. These results highlight that the interfaces may limit the lithium transport significantly in solid-state batteries. Fabrication of electrochemically active nanobatteries also enables in situ electron microscopy observation of electrochemical phenomena in a variety of solid-state battery chemistries.
Recursive prediction error methods for online estimation in nonlinear state-space models
Directory of Open Access Journals (Sweden)
Dag Ljungquist
1994-04-01
Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.
Solid-State Thermionic Power Generators: An Analytical Analysis in the Nonlinear Regime
Zebarjadi, M.
2017-07-01
Solid-state thermionic power generators are an alternative to thermoelectric modules. In this paper, we develop an analytical model to investigate the performance of these generators in the nonlinear regime. We identify dimensionless parameters determining their performance and provide measures to estimate an acceptable range of thermal and electrical resistances of thermionic generators. We find the relation between the optimum load resistance and the internal resistance and suggest guidelines for the design of thermionic power generators. Finally, we show that in the nonlinear regime, thermionic power generators can have efficiency values higher than the state-of-the-art thermoelectric modules.
Becis-Aubry, Yasmina; Boutayeb, Mohamed; Darouach, Mohamed
2006-01-01
International audience; This contribution proposes a recursive and easily implementable online algorithm for state estimation of multi-output discrete-time systems with nonlinear dynamics and linear measurements in presence of unknown but bounded disturbances corrupting both the state and measurement equations. The proposed algorithm is based on state bounding techniques and is decomposed into two steps : time update and observation update that uses a switching estimation Kalman-like gain mat...
Institute of Scientific and Technical Information of China (English)
FU Yu-sun; TIAN Zuo-hua; SHI Song-jiao
2001-01-01
The paper is concerned with the reliable H∞ state feedback control and controller parameterization problem for nonlinear systems with strictly redundant actuators. Based on Hamilton-Jacobi inequality,the sufficient condition is presented such that the reliable control problem is resolved, and a family of controllers is given such that the resulting closed-loop systems are asymptotically stable and their L2-gain is limitable not only when all actuators are operational but also when any one, but only one of actuators experiences an outage. The results of this paper provide a deep insight into the synthesis of the reliable nonlinear H∞ state-feedback.
Arens, S. J.; Sullivan, P. F.; Welker, J. M.; Rogers, M. C.; Holland, K.; Schimel, J.; Persson, K.
2006-12-01
Nutrient availability appears to be a controlling factor in the structure and function of High Arctic terrestrial systems as depicted by biological hot spots such as bird cliffs which are found throughout the arctic. Understanding the processes by which nutrients control plant production, canopy structure, and ecosystem carbon cycling have been well studied in the Low Arctic, where fertilization experiments have been employed for decades. Few studies have examined how the amount and type of nutrient augmentations (fertilization) affects the magnitude and pattern of CO2 exchange, species composition and optical properties of prostrate dwarf-shrub, herb tundra, the largest ecosystem in the High Arctic. In this study, amendments of three levels of nitrogen (N) (0.5 g/m2, 1.0 g/m2 and 5.0 g/m2) phosphorus (P) (2.5 g/m2) were initiated in prostrate dwarf- shrub, herb tundra near Pituffik (Thule), Greenland (76¢ªN, 68¢ªW). Species composition, net ecosystem CO2 exchange (NEE), gross primary photosynthesis (GPP), ecosystem respiration (ER) and plot-level normalized difference vegetation index (NDVI) were used to quantify changes in ecosystem structure and function. Non- linear responses to the addition of different levels of N were observed. CO2 gas exchange and NDVI showed indicated the strongest response at middle levels of N addition (1.0 g/m2). Strong and synergystic responses to the combined addition of nitrogen and phosphorus were observed. Increases in vegetation density and a shift in species composition were observed when N and P were added to these systems, partially explaining the near doubling of NDVI values from 0.3 to 0.6. Rates of NEE, GPP and ER were significantly higher when N and P were combined compared to independent additions of each or when compared to non-fertilized areas. Our results indicate that feedback processes such as CO2 exchange, optical properties and vegetation composition and structure are co-limited by N and P and that the addition
Thankappan, Aparna; Thomas, Sheenu; Nampoori, V. P. N.
2013-10-01
We report on the solvent effect on the third order optical nonlinearity of betanin natural dye extracted from red beet root and their third order nonlinear optical (NLO) properties have been studied using a Q-switched Nd:YAG laser at 532 nm. The third order nonlinearity of these samples are dominated by nonlinear absorption, which leads to strong optical limiting and their strength is influenced by the solvent used, suggesting that betanin natural dyes are promising candidate for the development of photonic nonlinear optic devices.
Prospects and limitations of mathematical methods for decision making in nonlinear complex systems
DEFF Research Database (Denmark)
Starke, Jens; Berkemer, Rainer
2007-01-01
This report discusses the art of scientific modeling in general. Different modeling approaches and their investigation are outlined. The final issue is to elaborate on the preconditions for utilizing mathematical models for decision making. We are very much indebted to the participants...... of the workshop Decision making and uncertainty in nonlinear complex systems for their valuable input on topics like uncertainty, nonlinearity, and complex systems in general. Scientists with different research backgrounds from various fields discussed several aspects of mathematical methods for decision making...... and strategic planning....
Prospects and limitations of mathematical methods for decision making in nonlinear complex systems
DEFF Research Database (Denmark)
Starke, Jens; Berkemer, Rainer
2007-01-01
of the workshop Decision making and uncertainty in nonlinear complex systems for their valuable input on topics like uncertainty, nonlinearity, and complex systems in general. Scientists with different research backgrounds from various fields discussed several aspects of mathematical methods for decision making......This report discusses the art of scientific modeling in general. Different modeling approaches and their investigation are outlined. The final issue is to elaborate on the preconditions for utilizing mathematical models for decision making. We are very much indebted to the participants...
Nonlinear closed loop optimal control: a modified state-dependent Riccati equation.
Rafee Nekoo, S
2013-03-01
The state-dependent Riccati equation (SDRE), as a controller, has been introduced and implemented since the 90s. In this article, the other aspects of this controller are declared which shows the capability of this technique. First, a general case which has control nonlinearities and time varying weighting matrix Q is solved with three approaches: exact solution (ES), online control update (OCU) and power series approximation (PSA). The proposed PSA in this paper is able to deal with time varying or state-dependent Q in nonlinear systems. As a result of having the solution of nonlinear systems with complex Q containing constraints, using OCU and proposed PSA, a method is introduced to prevent the collision of an end-effector of a robot and an obstacle which shows the adaptability of the SDRE controller. Two examples to support the idea are presented and conferred. Supplementing constraints to the SDRE via matrix Q, this approach is named a modified SDRE.
Boson-Faddeev in the Unitary Limit and Efimov States
K"\\ohler, H S
2010-01-01
A numerical study of the Faddeev equation for bosons is made with two-body interactions at or close to the Unitary limit. Separable interactions are obtained from phase-shifts defined by scattering length and effective range. In EFT-language this would correspond to NLO. Both ground and Efimov state energies are calculated. For effective ranges $r_0 > 0$ and rank-1 potentials the total energy $E_T$ is found to converge with momentum cut-off $\\Lambda$ for $\\Lambda > \\sim 10/r_0$ . In the Unitary limit ($1/a=r_0= 0$) the energy does however diverge. It is shown (analytically) that in this case $E_T=E_u\\Lambda^2$. Calculations give $E_u=-0.108$ for the ground state and $E_u=-1.\\times10^{-4}$ for the single Efimov state found. The cut-off divergence is remedied by modifying the off-shell t-matrix by replacing the rank-1 by a rank-2 phase-shift equivalent potential. This is somewhat similar to the counterterm method suggested by Bedaque et al. This investigation is exploratory and does not refer to any specific ph...
Srivastava, Nilabh; Haque, Imtiaz
2009-03-01
Over the past two decades, extensive research has been conducted on developing vehicle transmissions that meet the goals of reduced exhaust emissions and increased vehicle efficiency. A continuously variable transmission is an emerging automotive transmission technology that offers a continuum of gear ratios between desired limits. A chain CVT is a friction-limited drive whose dynamic performance and torque capacity rely significantly on the friction characteristic of the contact patch between the chain and the pulley. Although a CVT helps to maximize the vehicle fuel economy, its complete potential has not been accomplished in a mass-production vehicle. The present research focuses on developing models to analyze friction-induced nonlinear dynamics of a chain CVT drive and identify possible mechanisms that cause degradation of the overall dynamic performance by inducing chaos and self-sustained vibrations in the system. Two different mathematical models of friction, which characterize different operating or loading conditions, are embedded into a detailed planar multibody model of chain CVT in order to capture the various friction-induced effects in the system. Tools such as stick-slip oscillator dynamics, Lyapunov exponents, phase-space reconstruction, and recurrence plotting are incorporated to characterize the nonlinear dynamics of such a friction-limited system. The mathematical models, the computational scheme, and the results corresponding to different loading scenarios are discussed. The results discuss the influence of friction characteristics on the nonlinear dynamics and torque transmitting capacity of a chain CVT drive.
Nonlinear Optical Response of Disordered J Aggregates in the Motional Narrowing Limit
Knoester, Jasper
1995-01-01
We discuss the theory of nonlinear optical response of molecular aggregates with frequency disorder. In contrast to the usual modeling, we allow for spatial correlations in the disorder. We show that the joint distribution of all multi-exciton frequencies can be determined analytically to first orde
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
De Siena, S; Illuminati, F; Siena, Silvio De; Lisi, Antonio Di; Illuminati, Fabrizio
2002-01-01
We introduce nonlinear canonical transformations that yield effective Hamiltonians of multiphoton down conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton Hamiltonians. We study in detail the four-photon processes and the associated non-Gaussian four-photon squeezed states. The realization of squeezing, the behavior of the field statistics, and the structure of the phase space distributions show that these states realize a natural four-photon generalization of the two-photon squeezed states.
Projective limits of state spaces I. Classical formalism
Lanéry, Suzanne; Thiemann, Thomas
2017-01-01
In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski (1977) and Andrzej Okołów (2009, 2013, 2014), which describes the states of a quantum (field) theory as projective families of density matrices. A short reading guide to the series can be found in [27]. The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds [27, subsection 2.1]. In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them [27, subsection 4.1].
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the st
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Directory of Open Access Journals (Sweden)
Pabitra Pal Choudhury
2011-01-01
Full Text Available Dynamics of a nonlinear cellular automaton (CA is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.
Excited state nonlinear integral equations for an integrable anisotropic spin-1 chain
Energy Technology Data Exchange (ETDEWEB)
Suzuki, J [Department of Physics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka (Japan)
2004-12-17
We propose a set of nonlinear integral equations to describe the excited states of an integrable the spin-1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study of the supersymmetric sine-Gordon model.
Knaus, H.; Blab, G.; Agronskaia, A.V.; van den Heuvel, D.J.; Gerritsen, H.C.; Wösten, H.A.B.
2013-01-01
Label-free nonlinear spectral imaging microscopy (NLSM) records two-photon-excited fluorescence emission spectra of endogenous fluorophores within the specimen. Here, NLSM is introduced as a novel, minimally invasive method to analyze the metabolic state of fungal hyphae by monitoring the autofluore
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
Nonlinear Dependence of Global Warming Prediction on Ocean State
Liang, M.; Lin, L.; Tung, K. K.; Yung, Y. L.; Sun, S.
2010-12-01
Global temperature has increased by 0.8 C since the pre-industrial era, and is likely to increase further if greenhouse gas emission continues unchecked. Various mitigation efforts are being negotiated among nations to keep the increase under 2 C, beyond which the outcome is believed to be catastrophic. Such policy efforts are currently based on predictions by the state-of-the-art coupled atmosphere ocean models (AOGCM). Caution is advised for their use for the purpose of short-term (less than a century) climate prediction as the predicted warming and spatial patterns vary depending on the initial state of the ocean, even in an ensemble mean. The range of uncertainty in such predictions by Intergovernmental Panel on Climate Change (IPCC) models may be underreported when models were run with their oceans at various stages of adjustment with their atmospheres. By comparing a very long run (> 1000 years) of the coupled Goddard Institute for Space Studies (GISS) model with what was reported to IPCC Fourth Assessment Report (AR4), we show that the fully adjusted model transient climate sensitivity should be 30% higher for the same model, and the 2 C warming should occur sooner than previously predicted. Using model archives we further argue that this may be a common problem for the IPCC AR4 models, since few, if any, of the models has a fully adjusted ocean. For all models, multi-decadal climate predictions to 2050 are highly dependent on the initial ocean state (and so are unreliable). Such dependence cannot be removed simply by subtracting the climate drift from control runs.
Nonlinear state space model identification of synchronous generators
Energy Technology Data Exchange (ETDEWEB)
Dehghani, M.; Nikravesh, S.K.Y. [Electrical Engineering Department, Amirkabir University of Technology, Tehran (Iran)
2008-05-15
A method for identification of a synchronous generator is suggested in this paper. The method uses the theoretical relations of machine parameters and the Prony method to find the state space model of the system. Such models are useful for controller design and stability tests. The proposed identification method is applied to a third order model of a synchronous generator. In this study, the field voltage is considered as the input and the active output power and the rotor angle are considered as the outputs of the synchronous generator. Simulation results show good accuracy of the identified model. (author)
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Peng Guo
2012-12-01
Full Text Available With appropriate vibration modeling and analysis the incipient failure of key components such as the tower, drive train and rotor of a large wind turbine can be detected. In this paper, the Nonlinear State Estimation Technique (NSET has been applied to model turbine tower vibration to good effect, providing an understanding of the tower vibration dynamic characteristics and the main factors influencing these. The developed tower vibration model comprises two different parts: a sub-model used for below rated wind speed; and another for above rated wind speed. Supervisory control and data acquisition system (SCADA data from a single wind turbine collected from March to April 2006 is used in the modeling. Model validation has been subsequently undertaken and is presented. This research has demonstrated the effectiveness of the NSET approach to tower vibration; in particular its conceptual simplicity, clear physical interpretation and high accuracy. The developed and validated tower vibration model was then used to successfully detect blade angle asymmetry that is a common fault that should be remedied promptly to improve turbine performance and limit fatigue damage. The work also shows that condition monitoring is improved significantly if the information from the vibration signals is complemented by analysis of other relevant SCADA data such as power performance, wind speed, and rotor loads.
Li, Huaqing; Chen, Guo; Xiao, Li
2016-10-01
Event-triggered sampling control is motivated by the applications of embedded microprocessors equipped in the agents with limited computation and storage resources. This paper studied global consensus in multi-agent systems with inherent nonlinear dynamics on general directed networks using decentralised event-triggered strategy. For each agent, the controller updates are event-based and only triggered at its own event times by only utilising the locally current sampling data. A high-performance sampling event that only needs local neighbours' states at their own discrete time instants is presented. Furthermore, we introduce two kinds of general algebraic connectivity for strongly connected networks and strongly connected components of the directed network containing a spanning tree so as to describe the system's ability for reaching consensus. A detailed theoretical analysis on consensus is performed and two criteria are derived by virtue of algebraic graph theory, matrix theory and Lyapunov control approach. It is shown that the Zeno behaviour of triggering time sequence is excluded during the system's whole working process. A numerical simulation is given to show the effectiveness of the theoretical results.
The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
Dawes, Jonathan
2010-01-01
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of such problems, where a pattern-forming, or `Turing', instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. ...
Analysis and design for the second order nonlinear continuous extended states observer
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The extended state observer (ESO) is a novel observer for a class of uncertain systems. Since ESO adopts the continuous non-smooth structure, the classical observer design theory is hard to use for ESO analysis. In this note, the self-stable region (SSR) approach, which is a nonlinear synthesis method for nonlinear uncertain systems, will be used for ESO design and its stability analysis. The advantages of the non-smooth structure in ESO for improving the convergence properties and the estimation precision will be shown.
Nonlinear optics and solid-state lasers advanced concepts, tuning-fundamentals and applications
Yao, Jianquan
2012-01-01
This book covers the complete spectrum of nonlinear optics and all solid state lasers.The book integrates theory, calculations and practical design, technology, experimental schemes and applications. With the expansion and further development of Laser technology, the wavelength spectrum of Lasers had to be enlarged, even to be tunable which requires the use of nonlinear optical and Laser tunable technology. It systematically summarizes and integrates the analysis of international achievements within the last 20 years in this field. It will be helpful for university teachers, graduate students as well as engineers.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
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Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies
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Kairui Chen
2016-01-01
Full Text Available This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results.
Target reliability index for serviceability limit state of single piles
Institute of Scientific and Technical Information of China (English)
边晓亚; 郑俊杰; 徐志军; 章荣军
2015-01-01
The objective is to develop an approach for the determination of the target reliability index for serviceability limit state (SLS) of single piles. This contributes to conducting the SLS reliability-based design (RBD) of piles. Based on a two-parameter, hyperbolic curve-fitting equation describing the load−settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load−settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index (βsls) is obtained using the mean value first order second moment (MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation (MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement (slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimatesβsls compared to that computed by the MCS method. Besides, both factor of safety (FS) and slt are key factors influencingβsls, so the combination of FS andβsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.
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Baiyu Liu
2014-01-01
Full Text Available We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained.
Excited-state dynamics and nonlinear optical response of Ge nanocrystals embedded in silica matrix
Razzari, Luca; Gnoli, Andrea; Righini, Marcofabio; Dâna, Aykutlu; Aydinli, Atilla
2006-05-01
We use a dedicated Z-scan setup, arranged to account for cumulative effects, to study the nonlinear optical response of Ge nanocrystals embedded in silica matrix. Samples are prepared with plasma-enchanced chemical-vapor deposition and post-thermal annealing. We measure a third-order nonlinear refraction coefficient of γ =1×10-16m2/W. The nonlinear absorption shows an intensity-independent coefficient of β =4×10-10m/W related to fast processes. In addition, we measure a second β component around 10-9m /W with a relaxation time of 300μs that rises linearly with the laser intensity. We associate its origin to the absorption of excited carriers from a surface-defect state with a long depopulation time.
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Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Non-linear conductivity of NbS{sub 3} in pressure induced metal state
Energy Technology Data Exchange (ETDEWEB)
Dizhur, Eugene; Kostyleva, Irina; Voronovskii, Anatoly [Institute for High Pressure Physics of RAS, Kaluzhskoe sh. 14, 142190 Troitsk (Russian Federation); Zaitzev-Zotov, Sergey [Institute of Radioengineering and Electronics of the RAS, Mokhovaya ul. 11, 125009 Moscow (Russian Federation)
2011-05-15
Temperature and voltage dependencies of conduction of a quasi-one-dimensional conductor NbS{sub 3} after its transition into a metallic state has been studied at pressures higher than 6 GPa. The differential resistance R = dV /dI measured at small biases (the electric field E below 2 V/cm) demonstrate a considerable growth upon cooling below 20 K accompanied by appearance of the non-linear conduction. Both the growth and nonlinear conduction disappear at E > 3 V/cm or when the temperature exceeds 40 K. A narrow dip visible only at much smaller fields E < 20 mV/cm is superimposed over that nonlinear background when cooling below 3.7 K. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Energy Technology Data Exchange (ETDEWEB)
Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Directory of Open Access Journals (Sweden)
Gao Dexin
2012-10-01
Full Text Available This paper concentrates on the solution of state feedback exact linearization zero steady-state error optimal control problem for nonlinear systems affected by external disturbances. Firstly, the nonlinear system model with external disturbances is converted to quasi-linear system model by differential homeomorphism. Using Internal Model Optional Control (IMOC, the disturbances compensator is designed, which exactly offset the impact of external disturbances on the system. Taking the system and the disturbances compensator in series, a new augmented system is obtained. Then the zero steady-state error optimal control problem is transformed into the optimal regulator design problem of an augmented system, and the optimal static error feedback control law is designed according to the different quadratic performance index. At last, the simulation results show the effectiveness of the method.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
Nonadiabatic excited-state molecular dynamics: On-the-fly limiting of essential excited states
Nelson, Tammie; Naumov, Artem; Fernandez-Alberti, Sebastian; Tretiak, Sergei
2016-12-01
The simulation of nonadiabatic dynamics in extended molecular systems involving hundreds of atoms and large densities of states is particularly challenging. Nonadiabatic coupling terms (NACTs) represent a significant numerical bottleneck in surface hopping approaches. Rather than using unreliable NACT cutting schemes, here we develop "on-the-fly" state limiting methods to eliminate states that are no longer essential for the non-radiative relaxation dynamics as a trajectory proceeds. We propose a state number criteria and an energy-based state limit. The latter is more physically relevant by requiring a user-imposed energy threshold. For this purpose, we introduce a local kinetic energy gauge by summing contributions from atoms within the spatial localization of the electronic wavefunction to define the energy available for upward hops. The proposed state limiting schemes are implemented within the nonadiabatic excited-state molecular dynamics framework to simulate photoinduced relaxation in poly-phenylene vinylene (PPV) and branched poly-phenylene ethynylene (PPE) oligomers for benchmark evaluation.
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Esfandiar, H.
2013-05-01
Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.
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Il Young Song
2015-01-01
Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.
Projective limits of state spaces II. Quantum formalism
Lanéry, Suzanne; Thiemann, Thomas
2017-06-01
In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].
Vijayalakshmi, A.; Vidyavathy, B.; Vinitha, G.
2016-08-01
Isonicotinamide p-nitrophenol (ICPNP), a new organic material, was synthesized using methanol solvent. Single crystals of ICPNP were grown using a slow evaporation solution growth technique. Crystal structure of ICPNP is elucidated by single crystal X-ray diffraction analysis. It belongs to monoclinic crystal system with space group of P21/c. It forms two dimensional networks by O-H…O, N-H…O and C-H…O hydrogen bonds. The molecular structure of ICPNP was further confirmed by Fourier transform infrared (FTIR) spectral analysis. The optical transmittance range and the lower cut-off wavelength (421 nm) with the optical band gap (2.90 eV) of the ICPNP crystal were determined by UV-vis-NIR spectral study. Thermal behavior of ICPNP was studied by thermo gravimetric and differential thermal analyses (TG/DTA). The relative dielectric permittivity was calculated for various temperature ranges. Laser damage threshold of ICPNP crystal was found to be 1.9 GW/cm2 using an Nd:YAG laser. A Z-scan technique was employed to measure the nonlinear absorption coefficient, nonlinear refractive index and nonlinear optical susceptibility. Optical limiting behavior of ICPNP was observed at 35 mW input power.
Energy Technology Data Exchange (ETDEWEB)
Kobayashi, Yasuaki [Meme Media Laboratory, Hokkaido University, Sapporo 060-0813 (Japan); Kori, Hiroshi [Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610 (Japan)], E-mail: kobayashi@nsc.es.hokudai.ac.jp, E-mail: kori.hiroshi@ocha.ac.jp
2009-03-15
A theoretical framework is developed for the precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the analysis of a phase diffusion equation with global coupling. In particular, feedback functions that generate the following spatial patterns are analytically given: (i) 2-cluster states with an arbitrary population ratio, (ii) equally populated multi-cluster states and (iii) a desynchronized state. Our method is demonstrated numerically by using the Brusselator model in the oscillatory regime. Experimental realization is also discussed.
Gain Scheduling Control of Nonlinear Systems Based on Neural State Space Models
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Stoustrup, Jakob
2003-01-01
This paper presents a novel method for gain scheduling control of nonlinear systems based on extraction of local linear state space models from neural networks with direct application to robust control. A neural state space model of the system is first trained based on in- and output training...... samples from the system, after which linearized state space models are extracted from the neural network in a number of operating points according to a simple and computationally cheap scheme. Robust observer-based controllers can then be designed in each of these operating points,and gain scheduling...
Investigating Mesoscopic Non-linear Series Circuit with the Coherent Thermo State Representation
Wang, Xiu-Xia
2017-03-01
For the first time we considered the quantum effects of mesoscopic non-linear series circuit with the coherent thermo state representation | τ rangle . After introducing the representation |τ rangle , we derived the expression of the density matrix ρ and find that | ρ rangle T presents Gauss type with the representation | τ rangle . In addition, we derived the Wigner function and calculated the quantum fluctuation in the thermo vacuum state |0( β)>. It is shown that the circuit has the zero current fluctuation because the diode has the reverse saturation current, and the temperature affects the Wigner function of the circuit in thermo vacuum state deeply.
Static black holes in equilibrium with matter: nonlinear equation of state
Zaslavskii, Oleg B
2010-01-01
We consider a spherically symmetric black hole in equilibrium with surrounding classical matter that is characterized by a nonlinear dependence of the radial pressure p_{r} on the density {\\rho}. We examine under which requirements such an equilibrium is possible. It is shown that if the radial and transverse pressures are equal (Pascal perfect fluid), equation of state should be approximately linear near the horizon. The corresponding restriction on ((dp_{r})/(d{\\rho})) is a direct generalization of the result, previously found for an exactly linear equation of state. In the anisotropic case there is no restriction on equation of state but the horizon should be simple (nondegenerate).
Pre-Trained Neural Networks used for Non-Linear State Estimation
DEFF Research Database (Denmark)
Bayramoglu, Enis; Andersen, Nils Axel; Ravn, Ole
2011-01-01
The paper focuses on nonlinear state estimation assuming non-Gaussian distributions of the states and the disturbances. The posterior distribution and the aposteriori distribution is described by a chosen family of paramtric distributions. The state transformation then results in a transformation...... of the paramters in the distribution. This transformation is approximated by a neural network using offline training, which is based on monte carlo sampling. In the paper, there will also be presented a method to construct a flexible distributions well suited for covering the effect of the non...
Generation of squeezed-state superpositions via time-dependent Kerr nonlinearities
León-Montiel, R de J
2015-01-01
We put forward an experimental scheme for direct generation of optical squeezed coherent-state superpositions. The proposed setup makes use of an optical cavity, filled with a nonlinear Kerr medium, whose frequency is allowed to change during time evolution. By exactly solving the corresponding time-dependent anharmonic-oscillator Hamiltonian, we demonstrate that squeezed-state superpositions can be generated in an optical cavity. Furthermore, we show that the squeezing degree of the produced states can be tuned by properly controlling the frequency shift of the cavity, a feature that could be useful in many quantum information protocols, such as quantum teleportation and quantum computing.
Directory of Open Access Journals (Sweden)
Houda Salhi
2016-01-01
Full Text Available This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
Investigation of the effect of controllable dampers on limit states of rotor systems
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Zapoměl J.
2012-06-01
Full Text Available The unbalance and time varying loading are the principal sources of lateral vibrations of rotors and of increase of forces transmitted through the coupling elements into the stationary part. These oscillations and force effects can be considerably reduced if damping devices are added to the coupling elements placed between the rotor and its casing. The theoretical studies and practical experience show that to achieve their optimum performance their damping effect must be controllable. This article focuses on investigation of influence of controlled damping in the rotor supports on its limit state of deformation, fatigue failure and on magnitude of the forces transmitted into the stationary part. The analysed system is a flexible rotor with one disc driven by an electric DC motor and loaded by the disc unbalance and by technological forces depending on the rotor angular position. In the computational model the system vibration is governed by a set of nonlinear differential equations of the first and second orders. To evaluate the fatigue failure both the flexural and torsional oscillations are taken into account. The analysis is aimed at searching for the intervals of angular speeds, at which the rotor can be operated without exceeding the limit states.
Directory of Open Access Journals (Sweden)
Zongqi Liang
2009-01-01
Full Text Available We analyze a class of large time-stepping Fourier spectral methods for the semiclassical limit of the defocusing Nonlinear Schrödinger equation and provide highly stable methods which allow much larger time step than for a standard implicit-explicit approach. An extra term, which is consistent with the order of the time discretization, is added to stabilize the numerical schemes. Meanwhile, the first-order and second-order semi-implicit schemes are constructed and analyzed. Finally the numerical experiments are performed to demonstrate the effectiveness of the large time-stepping approaches.
Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung
2017-09-01
Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.
Liu, Qian; OuYang, Liangfei; Liang, Heng; Li, Nan; Geng, Xindu
2012-06-01
A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.
Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.
Chen, Ziting; Li, Zhijun; Chen, C L Philip
2016-03-17
An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
Robust control of a class of non-affine nonlinear systems by state and output feedback
Institute of Scientific and Technical Information of China (English)
陈贞丰; 章云
2014-01-01
Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers:the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded (UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.
A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials
Karrech, A.; Poulet, T.; Regenauer-Lieb, K.
2012-10-01
This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.
Nonlinear Sensing With Collective States of Ultracold Atoms in Optical Lattices
2015-04-02
decimation algorithm , a method that takes into account quantum correlations. B.1. In collaboration with D. Blume and X.Y. Yin at Washington State...Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Nonlinear quantum sensing, quantum metrology, ultracold atoms, optical lattices REPORT...with applications to interaction-based quantum metrology, Physical Review A, (10 2014): 0. doi: 10.1103/PhysRevA.90.041602 Khan W Mahmud, Lei Jiang
Interconnected delay and state observer for nonlinear systems with time-varying input delay
Léchappé, V; Moulay, Emmanuel; Plestan, F; Glumineau, A.
2016-01-01
International audience; This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.
Rabi oscillations of two-photon states in nonlinear optical resonators
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-02-01
We demonstrate that four-wave mixing processes in high-quality nonlinear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly antibunched photon states.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Solution of Macroscopic State Equations of Blume-Capel Model Using Nonlinear Dynamics Concepts
Directory of Open Access Journals (Sweden)
Asaf Tolga Ülgen
2013-01-01
Full Text Available The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.
An equation of state for granular media at the limit state of isotropic compression
Oquendo, W. F.; Muñoz, J. D.; Radjai, F.
2016-04-01
It is well believed that the volumetric entropy of Edwards captures part of the physics of granular media, but it is still unclear whether it can be applied to granular systems under mechanical stress. By working out a recent proposal by Aste, Di Matteo et al. to measure Edwards' compactivity from the volume distribution of Voronoï or Delaunay tessellations (Phys. Rev. E, 77 (2008) 021309), and assuming that the total volume divides into elementary cells of fixed minimal volume, we derive an equation of state relating the compactivity to the packing fraction, and we show by extensive molecular-dynamics simulations that this equation and its underlying assumption describe well the volumetric aspects of both the limit state of isotropic compression and the limit state of shear (also called critical state in soil mechanics) for three-dimensional ensembles of mono-disperse spheres, for a broad range of the sliding and rolling friction coefficients. In addition, by using the limit state of isotropic compression as testing ground, we find that the compactivity, the entropy per elementary cell and the number of elementary cells per grain computed by this method are the same within statistical precision, either by using Voronoï, Delaunay, or centroidal Voronoï tessellations, allowing thus for an objective definition. This means that not only Aste's cell method is robust and suitable to measure Edwards' compactivity of granular systems under mechanical stress but also the actual nature of the elementary cells might be unimportant.
Inferring gene regulatory networks via nonlinear state-space models and exploiting sparsity.
Noor, Amina; Serpedin, Erchin; Nounou, Mohamed; Nounou, Hazem N
2012-01-01
This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.
Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes
Institute of Scientific and Technical Information of China (English)
许锋; 汪晔晔; 罗雄麟
2013-01-01
Chemical processes are usually nonlinear singular systems. In this study, a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes, which are augmented as state variables. Based on the observability of the singular system, this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters. When the observability is satisfied, the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer. The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation. With the catalyst circulation rate as the only unknown input without model error, one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst cir-culation rate. However, when uncertain model parameters also exist, additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.
Liberty and the Limits to the Extraterrestrial State
Cockell, C. S.
The physical conditions that inhere in extraterrestrial environments have a tendency to drive society toward collectivist mechanisms of political and economic order to successfully cope with, and prevent possible disaster caused by, the lethal external conditions. Liberty will therefore be eroded by deliberate human action, through extraterrestrial authorities, and through a natural restriction in concepts of liberty that will attend the development and behaviour of people in confined environments. The emergence of extraterrestrial governance that nurtures liberty in outer space will require the formation of many institutions that encourage competition and reduce political and economic monopolies - with the legal system to sustain them. This problem is most clearly manifest in oxygen production. These considerations allow the purpose and limits of the extraterrestrial state and precursor forms of governance to be circumscribed. Far from being a purely speculative enquiry, this discussion allows requirements in physical architecture and social organisation to be identified that can be considered from the earliest stages of space exploration and settlement.
Nonlinear fiber gyroscope for quantum metrology
Luis, Alfredo; Rivas, Ángel
2016-01-01
We examine the performance of a nonlinear fiber gyroscope for improved signal detection beating the quantum limits of its linear counterparts. The performance is examined when the nonlinear gyroscope is illuminated by practical field states, such as coherent and quadrature squeezed states. This is compared with the case of more ideal probes such as photon-number states.
Nonlinear fiber gyroscope for quantum metrology
Luis, Alfredo; Morales, Irene; Rivas, Ángel
2016-07-01
We examine the performance of a nonlinear fiber gyroscope for improved signal detection beating the quantum limits of its linear counterparts. The performance is examined when the nonlinear gyroscope is illuminated by practical field states, such as coherent and quadrature squeezed states. This is compared with the case of more ideal probes such as photon-number states.
A Neural-Network-Based Nonlinear Adaptive State-Observer for Pressurized Water Reactors
Directory of Open Access Journals (Sweden)
Zhe Dong
2013-10-01
Full Text Available Although there have been some severe nuclear accidents such as Three Mile Island (USA, Chernobyl (Ukraine and Fukushima (Japan, nuclear fission energy is still a source of clean energy that can substitute for fossil fuels in a centralized way and in a great amount with commercial availability and economic competitiveness. Since the pressurized water reactor (PWR is the most widely used nuclear fission reactor, its safe, stable and efficient operation is meaningful to the current rebirth of the nuclear fission energy industry. Power-level regulation is an important technique which can deeply affect the operation stability and efficiency of PWRs. Compared with the classical power-level controllers, the advanced power-level regulators could strengthen both the closed-loop stability and control performance by feeding back the internal state-variables. However, not all of the internal state variables of a PWR can be obtained directly by measurements. To implement advanced PWR power-level control law, it is necessary to develop a state-observer to reconstruct the unmeasurable state-variables. Since a PWR is naturally a complex nonlinear system with parameters varying with power-level, fuel burnup, xenon isotope production, control rod worth and etc., it is meaningful to design a nonlinear observer for the PWR with adaptability to system uncertainties. Due to this and the strong learning capability of the multi-layer perceptron (MLP neural network, an MLP-based nonlinear adaptive observer is given for PWRs. Based upon Lyapunov stability theory, it is proved theoretically that this newly-built observer can provide bounded and convergent state-observation. This observer is then applied to the state-observation of a special PWR, i.e., the nuclear heating reactor (NHR, and numerical simulation results not only verify its feasibility but also give the relationship between the observation performance and observer parameters.
Entangler and analyzer for multiphotonGreenberger-Horne-Zeilinger states using weak nonlinearities
Institute of Scientific and Technical Information of China (English)
DING Dong; YAN FengLi; GAO Ting
2014-01-01
In the regime of weak nonlinearity we present two general,feasible schemes for manipulating photon states.One is an entangler for generating any one of the n-photon Greenberger-Home-Zeilinger (GHZ) states.Interactions of the incoming photons with crossKerr media followed by a phase shift gate and a measurement on a probe beam plus appropriate local operations using classical feed-forward of the measurement results allow one to obtain the desired states in a nearly deterministic manner.The second scheme discussed is an analyzer for multiphoton maximally entangled states,which is derived from the above entangler.In this scheme,all of the 2n n-photon GHZ states can,nearly deterministically,be discriminated.
Selective measurement of quantronium qubit states by using of mesoscopic non-linear oscillator
Denisenko, M. V.; Satanin, A. M.
2016-12-01
We study the process of selective measurements of states of individual quantum systems - Josephson qubit - using nonlinear oscillator, working in the mesoscopic regime, when the number of quanta in the measuring process varies from a few dozen to a few hundred. Quantum Monte-Carlo method simulated dissipative dynamics of the system "qubit - oscillator" and the measurement process of a qubit state to modify the number of quanta of the oscillator. It is shown that for different Rabi-pulses of the recording state of a qubit the discrimination of states is possible, as well as the measurement of the effect of back-action of the measuring device, including separation of the prepared superposition state - carrying out statistical projective measurements.
Nonlinear Adaptive Descriptor Observer for the Joint States and Parameters Estimation
2016-08-29
In this note, the joint state and parameters estimation problem for nonlinear multi-input multi-output descriptor systems is considered. Asymptotic convergence of the adaptive descriptor observer is established by a sufficient set of linear matrix inequalities for the noise-free systems. The noise corrupted systems are also considered and it is shown that the state and parameters estimation errors are bounded for bounded noises. In addition, if the noises are bounded and have zero mean, then the estimation errors asymptotically converge to zero in the mean. The performance of the proposed adaptive observer is illustrated by a numerical example.
Amir, Naila; Iqbal, Shahid
2017-08-01
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.
Institute of Scientific and Technical Information of China (English)
Meng Xiang-Guo; Wang Ji-Suo; Liu Tang-Kun
2008-01-01
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states(EONLPCSs),which can be realized via operating the superposed evolution operators D±(τ)on the state |q,0),is constructed,then their orthonormalized property,completeness relations and some nonclassical properties are discussed.It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations.Moreover,the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ξ.
Rudra, Shubhobrata; Barai, Ranjit Kumar; Maitra, Madhubanti
2014-03-01
This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.
Mircea, Dragos I.; Anlage, Steven M.
2004-03-01
Traditionally, the Andreev Bound States (ABS) have been studied by means of tunneling experiments and global electromagnetic resonant techniques. The zero bias conductance peak and the strong upturn in the penetration depth at low temperature are considered strong evidence for the existence of ABS. The nonlinear inductance arising from the current-dependent penetration depth leads to a nonlinear electrodynamic response that can be probed with our non-resonant near-field microwave microscope [S. C. Lee and S. M. Anlage, Appl. Phys. Lett. 82, 1893 (2003)]. In the experiment, microwave currents have been applied locally along different directions on the surface of YBCO films exposing the (110) surface in order to investigate the angular dependence of the second and third order harmonics generated by the sample. The temperature and the angular dependence measured for different levels of the applied microwave power, will be presented and compared with the theoretical predictions. This low-temperature anisotropic nonlinear behavior is relevant for the study of ABS as well as for identifying the existence of local pairing states with symmetry different from that of the bulk order parameter.
Nonlinear neural network for hemodynamic model state and input estimation using fMRI data
Karam, Ayman M.
2014-11-01
Originally inspired by biological neural networks, artificial neural networks (ANNs) are powerful mathematical tools that can solve complex nonlinear problems such as filtering, classification, prediction and more. This paper demonstrates the first successful implementation of ANN, specifically nonlinear autoregressive with exogenous input (NARX) networks, to estimate the hemodynamic states and neural activity from simulated and measured real blood oxygenation level dependent (BOLD) signals. Blocked and event-related BOLD data are used to test the algorithm on real experiments. The proposed method is accurate and robust even in the presence of signal noise and it does not depend on sampling interval. Moreover, the structure of the NARX networks is optimized to yield the best estimate with minimal network architecture. The results of the estimated neural activity are also discussed in terms of their potential use.
Effect of dielectric medium on the nonclassical properties of nonlinear sphere coherent states
Directory of Open Access Journals (Sweden)
E Amooghorban
2014-04-01
Full Text Available In order to investigate the effect of a medium with dissipation and dispersion and also the curvature of the physical space on the properties of the incident quantum states, we use the quantization of electromagnetic field based on phenomenological approach to obtain input-output relations between radiations on both sides of dielectric slab. By using these relations the fidelity, the Wigner function, and also the quantum correlation of the outgoing state through dielectric slab are obtained for a situation in which the rightward incident state is a nonlinear coherent state on a sphere and the leftward incident state is a vacuum state. Here, the incident states are considered monochromatic and the modeling of the medium is given by the Lorentz' model. Accordingly, we study nonclassical properties of the output states such as the quantum entanglement. It will be observed that the nonclassical properties of the outgoing states depend strongly on the optical property of the medium and also on the curvature of the physical state.
Arefi, Mohammad Mehdi; Jahed-Motlagh, Mohammad Reza; Karimi, Hamid Reza
2015-08-01
In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.
Liu, Yan-Jun; Li, Jing; Tong, Shaocheng; Chen, C L Philip
2016-07-01
In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.
Improved Limit on Direct α Decay of the Hoyle State
DEFF Research Database (Denmark)
Kirsebom, Oliver Sølund; Alcorta, M.; Borge, M.J.G.
2012-01-01
The current evaluation of the triple-α reaction rate assumes that the α decay of the 7.65 MeV, 0+ state in 12C, commonly known as the Hoyle state, proceeds sequentially via the ground state of 8Be. This assumption is challenged by the recent identification of two direct α-decay branches with a co...
Improved Limit on Direct α Decay of the Hoyle State
DEFF Research Database (Denmark)
Kirsebom, Oliver Sølund; Alcorta, M.; Borge, M.J.G.
2012-01-01
The current evaluation of the triple-α reaction rate assumes that the α decay of the 7.65 MeV, 0+ state in 12C, commonly known as the Hoyle state, proceeds sequentially via the ground state of 8Be. This assumption is challenged by the recent identification of two direct α-decay branches with a co...
Proposition 76: State Spending and School Funding Limits. Voter Guide
EdSource, 2005
2005-01-01
On Nov. 8, 2005, California voters will decide whether to pass Proposition 76, known as the "Live Within Our Means Act." Sponsored by Gov. Arnold Schwarzenegger, the measure seeks to address state budget problems that have been particularly severe in California since 2002 due to cuts in state taxes and increases in state expenditures.…
Zalian, Cyrus
2016-01-01
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This dis...
Third-Order Nonlinear Optic and Optical Limiting Properties of a Mn(iii) Transition Metal Complex
Karakas, Asli; Elmali, Ayhan; Yahsi, Yasemin; Kara, Hulya
N,N‧-bis(5-bromosalicylidene)propane-1,2-diamine-O,O‧,N,N‧)-manganese(III) chloride transition metal complex has been synthesized and characterized by elemental analysis and UV-vis spectroscopy. Its crystal structure has been determined using X-ray diffraction analysis. To provide an insight into the optical limiting (OL) behavior of the title compound, the third-order nonlinear optical (NLO) properties, one-photon absorption (OPA) and two-photon absorption (TPA) characterizations have been theoretically investigated by means of the time-dependent Hartree-Fock (TDHF), AM1 and configuration interaction (CI) methods, respectively. According to ab initio calculation results, the examined molecule exhibits second hyperpolarizabilities (γ) with non-zero values at the positions of TPA peaks, implying microscopic third-order optical nonlinearity. The maximum OPA wavelengths recorded by linear optical experiment and quantum mechanical computations are estimated in the UV region to be shorter than 400 nm, showing good optical transparency to the visible light. The TPA cross-sections (δ(ω)) at λ max(2) values indicate that the synthesized compound might possess OL phenomena, which are in accord with the experimental observations on the manganese complexes in the literature.
Niemi, Jarad; West, Mike
2010-06-01
We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.
Consensus Control of Nonlinear Multiagent Systems With Time-Varying State Constraints.
Meng, Wenchao; Yang, Qinmin; Si, Jennie; Sun, Youxian
2016-12-01
In this paper, we present a novel adaptive consensus algorithm for a class of nonlinear multiagent systems with time-varying asymmetric state constraints. As such, our contribution is a step forward beyond the usual consensus stabilization result to show that the states of the agents remain within a user defined, time-varying bound. To prove our new results, the original multiagent system is transformed into a new one. Stabilization and consensus of transformed states are sufficient to ensure the consensus of the original networked agents without violating of the predefined asymmetric time-varying state constraints. A single neural network (NN), whose weights are tuned online, is used in our design to approximate the unknown functions in the agent's dynamics. To account for the NN approximation residual, reconstruction error, and external disturbances, a robust term is introduced into the approximating system equation. Additionally in our design, each agent only exchanges the information with its neighbor agents, and thus the proposed consensus algorithm is decentralized. The theoretical results are proved via Lyapunov synthesis. Finally, simulations are performed on a nonlinear multiagent system to illustrate the performance of our consensus design scheme.
Korayem, M H; Nekoo, S R
2015-07-01
This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data.
Optical limiting and nonlinear optical properties of gold-decorated graphene nanocomposites
Podila, Ramakrishna; Pradhan, Prabin; Molli, Muralikrishna; Kaniyoor, Adarsh; Muthukumar v, Sai; Sai, S. Siva Sankara; Ramaprabhu, S.; Rao, Apparao; Department of Physics, Sri Sathya Sai Institute of Higher Learning Team; Alternative Energy; Nanotechnology Laboratory (AENL), Indian Institute of Technology Madras Team; Department of Physics; Astronomy, Clemson Nanomaterials Center, Clemson University Team
2015-03-01
Although metal nanoparticle-decorated nanomaterials exhibit excellent optical limiting (OL) performance at a relatively higher fluence (>9 J/cm2) , there is a dearth of OL materials for protecting low damage threshold (metal d-orbitals and graphene p-orbitals often leads to undesirable changes in graphene's electronic structure, which adversely affects OL. Here, we demonstrate that d-orbitals of Au nanoparticles exhibit little or no rehybridization with graphene, and result in an enhanced OL behavior even at a low fluence of ~ 0.4 J/cm2 due to the excellent photo-absorption of Au combined with rapid carrier thermalization by graphene.
Institute of Scientific and Technical Information of China (English)
Lidong Lü; Yuejiang Song; Fan Zhu; Xuping Zhang
2012-01-01
The nonlinear effects that limit the performance of the multi-frequency probe (MFP) based coherent optical time domain reflectometry (C-OTDR) are investigated.Based on theoretical analysis and experimental results,compared with conventional C-OTDR,when the probe pulse has power gradient within the pulse width,self-phase modulation (SPM) and cross-phase modulation (XPM) are strengthened in the new COTDR scheme.The generation of four-wave mixing (FWM) is dependent on SPM and XPM,and with modulation frequency of phase modulator higher than 40 MHz,the stimulated Brillouin scattering (SBS) threshold can be enhanced by more than 5 dB,which benefits the maximum dynamic range of the MFP C-OTDR.
Directory of Open Access Journals (Sweden)
Maruthai Suresh
2010-10-01
Full Text Available A nonlinear process, the heat exchanger whose parameters vary with respect to the process variable, is considered. The time constant and gain of the chosen process vary as a function of temperature. The limitations of the conventional feedback controller tuned using Ziegler-Nichols settings for the chosen process are brought out. The servo and regulatory responses through simulation and experimentation for various magnitudes of set-point changes and load changes at various operating points with the controller tuned only at a chosen nominal operating point are obtained and analyzed. Regulatory responses for output load changes are studied. The efficiency of feedforward controller and the effects of modeling error have been brought out. An IMC based system is presented to understand clearly how variations of system parameters affect the performance of the controller. The present work illustrates the effectiveness of Feedforward and IMC controller.
Monthus, Cécile
2004-02-01
We study the dynamics in the one-dimensional disordered trap model with a broad distribution of trapping times p(tau) approximately 1/tau(1+mu), when an external force is applied from the very beginning at t=0, or only after a waiting time t(w), in the linear as well as in the nonlinear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder mu-->0, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in detail the various regimes that exist for the average position in terms of the two times and the external field.
2011-04-29
... States; Highly Migratory Species Fisheries; Annual Catch Limits and Accountability Measures AGENCY... annual catch limits (ACLs) and accountability measures (AMs). This proposed rule to implement Amendment 2... have any direct or indirect socioeconomic impacts, because harvest limits and management...
2010-07-20
... United States; Northeast Multispecies Fishery; Pollock Catch Limit Revisions AGENCY: National Marine... associated increases in pollock catch limits under the Northeast (NE) Multispecies Fishery Management Plan..., including Overfishing Levels (OFLs), Acceptable Biological Catches (ABCs), Annual Catch Limits (ACLs),...
Non-Linear Trans-Planckian Corrections of Spectra due to the Non-trivial Initial States
Yusofi, E
2014-01-01
Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space-time as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods.
Inverse solution technique of steady-state responses for local nonlinear structures
Wang, Xing; Guan, Xin; Zheng, Gangtie
2016-03-01
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Observer-Based Control Design for Nonlinear Networked Control Systems with Limited Information
Directory of Open Access Journals (Sweden)
Yilin Wang
2013-01-01
Full Text Available This paper is concerned with the problem of designing a robust observer-based controller for discrete-time networked systems with limited information. An improved networked control system model is proposed and the effects of random packet dropout, time-varying delay, and quantization are considered simultaneously. Based on the obtained model, a stability criterion is developed by constructing an appropriate Lyapunov-Krasovskii functional and sufficient conditions for the existence of a dynamic quantized output feedback controller which are given in terms of linear matrix inequalities (LMIs such that the augmented error system is stochastically stable with an performance level. An example is presented to illustrate the effectiveness of the proposed method.
Institute of Scientific and Technical Information of China (English)
王自东; 胡汉起
1997-01-01
The nonlinear dynamics equations of the time dependence of the perturbation amplitude of the solid/ liquid interface during unidirectional solidification of a dilute binary alloy are established. The solutions to these equations are obtained, and the condition of the initial steady state growth of the cellular and dendritic structure after the planar solid/liquid interface bifurcates (mGc> G) with the increase of the growth rate is given. The condition of the steady state growth of fine cellular and dendritic structure in the beginning after the coarse dendrites bifurcate ( mGc<Γw2 + G) under the rapid solidification is obtained. The relationship of the steady state cell and dendrite tip radius, the perturbation amplitude and wavelength at the solid/liquid interface is presented.
Phase sensitivity in deformed-state superposition considering nonlinear phase shifts
Berrada, K.
2016-07-01
We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
Miao, Zhiyong; Shi, Hongyang; Zhang, Yi; Xu, Fan
2017-10-01
In this paper, a new variational Bayesian adaptive cubature Kalman filter (VBACKF) is proposed for nonlinear state estimation. Although the conventional VBACKF performs better than cubature Kalman filtering (CKF) in solving nonlinear systems with time-varying measurement noise, its performance may degrade due to the uncertainty of the system model. To overcome this drawback, a multilayer feed-forward neural network (MFNN) is used to aid the conventional VBACKF, generalizing it to attain higher estimation accuracy and robustness. In the proposed neural-network-aided variational Bayesian adaptive cubature Kalman filter (NN-VBACKF), the MFNN is used to turn the state estimation of the VBACKF adaptively, and it is used for both state estimation and in the online training paradigm simultaneously. To evaluate the performance of the proposed method, it is compared with CKF and VBACKF via target tracking problems. The simulation results demonstrate that the estimation accuracy and robustness of the proposed method are better than those of the CKF and VBACKF.
Sakho, El hadji Mamour; Oluwafemi, Oluwatobi S.; Sreekanth, P.; Philip, Reji; Thomas, Sabu; Kalarikkal, Nandakumar
2016-08-01
Nonlinear optical (NLO) response under near infrared (800 nm) and visible (532 nm) laser excitations, of 100 fs (fs) and 5 ns (ns) pulse durations respectively, of reduced graphene oxide (RGO), non-covalent functionalized reduced graphene oxide (NF-RGO) and NF-RGO decorated with various concentration of silver nanoparticles (NF-RGO/Ag-NPs) have been investigated using the Open-aperture Z-Scan technique. For both femtosecond and nanosecond laser excitations, the studied graphene-based materials exhibit good nonlinear optical power limiting properties (OL), with NF-RGO/Ag-NPs sample prepared with 0.1 M AgNO3 showing the best nonlinear optical properties. For the ns regime, the optical limiting threshold decreased from 8.3 J/cm2 in NF-RGO to 4.3 J/cm2 in NF-RGO/Ag-NPs, while at fs regime, the nonlinear absorption coefficient (β) was found to increase with decrease in concentration of Ag-NPs in the hybrid. Two-photon absorption (2 PA) in combination with saturable absorption (SA) in femtosecond regime, and reverse saturable absorption (RSA) along with saturable absorption (SA) in the nanosecond regime, are responsible for the observed nonlinear optical absorption (NLA) behavior in these materials. These findings show that the as-synthesized NF-RGO/Ag-NPs hybrid is a relatively better material for nonlinear optical limiting applications.
Maritime Limits and Boundaries of United States of America
National Oceanic and Atmospheric Administration, Department of Commerce — NOAA is responsible for depicting on its nautical charts the limits of the 12 nautical mile Territorial Sea, 24 nautical mile Contiguous Zone, and 200 nautical mile...
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-06-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ ^2 u_{xx} +V'(u) =0 \\quad x\\in [0,1] where κ >0 is a parameter and V( u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2, there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ , however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-01-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ^2 u_{xx} +V'(u) =0 quad xin [0,1] where κ >0 is a parameter and V(u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2 , there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ, however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Institute of Scientific and Technical Information of China (English)
CHEN Ming-jie; LI Dian-pu; ZHANG Ai-jun
2004-01-01
Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In this paper, a universal nonlinear stateobserver is presented for a class of universal chaotic systems to realize the chaotic synchronization, according to the theory of state-observer in the modern control theory. And theoretic analysis and simulation results have illustrated the validity of the approach. Moreover, the approach of synchronization proposed in this paper is very easy, flexible and universal with high synchronization precision.When the approach is applied to secure communication, the results are satisfying.
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.
2015-01-01
In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP...
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 ... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations....
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a new type of base isolation system, i.e., slide-limited friction (S-LF) base isolation system. Based on this system, the harmonic and subharmonic periodic response of S-LF subjected to harmonic motions is investigated by using Fourier-Galerkin-Newton (FGN) method with Floquet theory. The dynamic response of S-LF subjected to earthquake ground motions is calculated with a high order precision direct integration method, and the numerical results are presented in maximum acceleration response spectra of superstructure and maximum sliding displacement response spectrum form. The comparison of isolating effects of S-LF, pure-friction base isolation system (P-F) and resilient-friction base isolation system (R-FBI) shows that the isolating property of S-LF is superior to those of P-F and R-FBI. Finally, by analyzing an engineering example, it is observed that the distribution of the maximum shear between floors and absolute acceleration of S-LF to earthquake ground motion is very different from that of traditional structures.
Geometry and large N limits in Laughlin states
Klevtsov, Semyon
2016-01-01
In these notes I survey geometric aspects of the lowest Landau level wave functions, integer quantum Hall state and Laughlin states on compact Riemann surfaces. In particular, I review geometric adiabatic transport on the moduli spaces, derivation of the electromagnetic and gravitational anomalies, Chern-Simons theory and adiabatic phase, and the relation to holomorphic line bundles, Quillen metric, regularized spectral determinants, bosonisation formulas on Riemann surfaces and asymptotic expansion of the Bergman kernel.
Institute of Scientific and Technical Information of China (English)
Qiang Zheng; Yi-hu Song; Xiao-su Yi
2001-01-01
The nonlinear J-E characteristics under self-heating equilibrium for conductive composites based on high density polyethylene were studied. The results show that there are identical conduction mechanisms under self-heating equilibrium for the composites with various initial resistivities determined by filler content or ambient temperature. The nonlinear conduction behavior was involved in the limited microstructure transformations of the conducting network induced by electrical field applied and the corresponding self-heating effect. A reversible thermal fuse (RTF) model was suggested to interpret the physical origin of the nonlinear J-E characteristics.
Energy Technology Data Exchange (ETDEWEB)
Kharkovskiy, A. I., E-mail: akharkovskiy@inbox.ru [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); L.F. Vereshchagin Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow (Russian Federation); Shaldin, Yu. V. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); Institute for Crystallography RAS, Lenin' s Avenue 59, 119333 Moscow (Russian Federation); Nizhankovskii, V. I. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland)
2016-01-07
The direct nonlinear magnetoelectric (ME) effect and the magnetostriction of piezoelectric CsCuCl{sub 3} single crystals were comprehensively studied over a wide temperature range in stationary magnetic fields of up to 14 T. The direct nonlinear ME effect measurements were also performed in pulsed magnetic fields up to 31 T, at liquid helium temperature in the antiferromagnetic (AF) state for the crystallographic direction in which effect has the maximum value. The nonlinear ME effect was quadratic in the paramagnetic state for the whole range of magnetic fields. In the AF state the phase transition between different configurations of spins manifested itself as plateau-like peculiarity on the nonlinear ME effect. The nonlinear ME effect was saturated by the phase transition to the spin-saturated paramagnetic state. Two contributions to the nonlinear ME effects in CsCuCl{sub 3} were extracted from the experimental data: the intrinsic ME effect originated from the magnetoelectric interactions, and the extrinsic one, which resulted from a magnetostriction-induced piezoelectric effect.
Directory of Open Access Journals (Sweden)
Wenjie Qin
2014-01-01
Full Text Available The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.
Muruganandi, G.; Saravanan, M.; Vinitha, G.; Jessie Raj, M. B.; Sabari Girisun, T. C.
2017-05-01
Reduced graphene oxide (rGO) was prepared by reduction method using various reductants like hydrazine, sodium borohydride and ascorbic acid. XRD and Raman analysis confirmed the effective removal of functional groups in GO. SEM revealed that rGO consists of thin crumpled and disordered sheets closely associated with each other. Blue shift in UV-absorption maxima was due to weak interlayer coupling between the layers of rGO. Third order NLO properties of dispersed rGO were measured by Z-scan technique (532 nm, 50 mW). Both GO and rGO possess self defocusing, saturable absorption and optical limiting behavior. The nonlinear component of refractive index, absorption coefficient and optical susceptibility were found to be 10-8 cm2/W, 10-3 cm/W and 10-6 esu respectively. Tunability of NLO coefficients with altering functional groups upon rGO was achieved. rGO prepared using hydrazine with high NLO coefficient and excellent durability, signify the scope of utilizing them as optical limiters.
Fault current limiter with solid-state circuit breakers
Bălan, H.; Neamț, L.; Buzdugan, M. I.; Varodi, T.; Pop, E.
2016-08-01
Switching of power circuit breakers is an important technical issue, especially at short circuit, since the fault current cause thermal and dynamic stresses, and the power quality worsens. Recently, the development of distributed renewable electricity induces the short circuit protection problematic because the distributed production of electric energy cause the transport networks to lose their radial character and disturbs the protective relays coordination. The modern technologies for power switching uses static fault current limiters, which offers a viable solution to remove the problems caused by large fault currents in the system. An appropriate design of the current limiting device reduces the thermal and dynamic stress and limits the fault current to a low value. The static switches are based on high power semiconductor devices that offer advantages compared to mechanical switches. Using a fault current limiter that minimizes the effect of distributed generation of electricity in a radial network on the co-ordination of protective relays is a solution to this problem in terms of switching speed and lifespan of power switches.
About limit matrices of finite-state Markov chains
Nieuwenhuis, J.W.
1997-01-01
By means of the concept of group inverse of a matrix we study limiting properties of a collection of stochastic matrices {P-epsilon, epsilon is an element of [0, 1]}, where For All epsilon is an element of [0, 1], P-epsilon is an element of R(nxn) and where P-0 = lim(epsilon-->0)P(epsilon). (C) Else
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang
2012-01-01
We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...
Chandra Shekhara Shetty, T.; Chidan Kumar, C. S.; Gagan Patel, K. N.; Chia, Tze Shyang; Dharmaprakash, S. M.; Ramasami, Ponnadurai; Umar, Yunusa; Chandraju, Siddegowda; Quah, Ching Kheng
2017-09-01
Two new chalcones namely, (2E)-1-(3-fluoro-4-methoxyphenyl)-3-(4-methoxyphenyl) prop-2-en-1-one and (2E)-3-(4-chlorophenyl)-1-(3-fluoro-4-methoxyphenyl)prop-2-en-1-one were synthesized and grown as single crystals by slow evaporation technique in methanol. The FTIR spectrum recorded confirms the presence of functional groups in these materials. The molecular conformation of the compounds was achieved by single crystal X-ray diffraction studies. The thermal stability of the crystals was determined from TGA/DSC curve. The third order optical nonlinearity of the chalcone compounds in DMF solution has been carried out using an Nd:YAG laser at 532 nm as the source of excitation. The nonlinear optical response was characterized by measuring the intensity dependent refractive index n2 of the medium using Z-scan technique. It is seen that the molecules exhibit a negative (defocusing) nonlinearity and large nonlinear refractive index of the order of -1.8 × 10-11 esu. The third-order nonlinearity of the studied chalcones is dominated by nonlinear refraction, which leads to strong optical limiting of laser. The result reveals that these two new chalcone molecules would be a promising material for optical limiting applications. In addition, the optimized molecular geometry, vibrational frequencies in gas, and the Molecular Electrostatic Potential (MEP) surface parameters of the two molecules were calculated using DFT/B3LYP method with 6-311++G(d,p) basis set in ground state. All the theoretical calculations were found in good agreement with experimental data.
Rudra, Shubhobrata; Maitra, Madhubanti
2017-01-01
This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...
Nonlinear response and two stable electroconducting states in transparent plasticized PVC films
Vlasov, D. V.; Apresyan, L. A.; Vlasova, T. V.; Kryshtob, V. I.
2010-10-01
The electric conductivity of transparent plasticized poly(vinyl chloride) (PVC) films with thicknesses about 30-50 μm has been studied in electric fields with strengths significantly below the breakdown level. It is established that the PVC films exhibit spontaneous reversible transitions between two stable states—with high and relatively low conductivities, in which the bulk resistivity amounts to ˜103 and 106 Ω m, respectively. Relaxation current-voltage characteristics have been measured in a continuous regime, which allowed the Debye relaxation processes to be taken into consideration and effects related to the nonlinearity and transitions between indicated states to be separated. A regime with deterministic switching between the two conducting states has been observed. A simple qualitative model that describes the anomalous character of conductivity in polymer films is proposed.
Computation of Value Functions in Nonlinear Differential Games with State Constraints
Botkin, Nikolai
2013-01-01
Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.
Cohen, S.A.; Hosea, J.C.; Timberlake, J.R.
1984-10-19
A limiter with a specially contoured front face is provided. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution. This limiter shape accommodates the various power scrape-off distances lambda p, which depend on the parallel velocity, V/sub parallel/, of the impacting particles.
Joannin, Colas; Chouvion, Benjamin; Thouverez, Fabrice; Ousty, Jean-Philippe; Mbaye, Moustapha
2017-01-01
This paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.
Non-linear states of a positive or negative refraction index material in a cavity with feedback
Mártin, D. A.; Hoyuelos, M.
2010-06-01
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrödinger equations for the electric and magnetic field amplitudes.
Directory of Open Access Journals (Sweden)
Guowei Cai
2014-01-01
Full Text Available As to strong nonlinearity of doubly fed induction generators (DFIG and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC. The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
State variable participation in the limit cycle of induction motor
Indian Academy of Sciences (India)
Krishnendu Chakrabarty; Urmila Kar
2015-03-01
The paper presents bifurcation behaviour of a single-phase induction motor. Study of bifurcation of a system gives the complete picture of its dynamical behaviour with the change in system’s parameters. The system is mathematically described by a set of differential equations in the state space. Induction motors are very widely used in domestic and commercial applications. Single-phase capacitor-run induction motors are commonly used as prime movers for fans, pumps and compressors. This paper provides a numerical approach to understand the dynamics of an induction motor in the light of bifurcation and chaos. It is seen that the dynamics of a capacitor-run single-phase induction motor cannot be ascertained by the profile of a single state variable. This paper also attempts to discuss the bifurcation behaviour of the system based on the evolution of different state variables. The bifurcation diagrams drawn looking at different state variables are different in terms of periodicity and route to chaos. The knowledge of the dynamics of the system obtained from bifurcation diagrams give useful guidelines to control the operation of the induction motor depending on the need of an application for better performance.
Projective Limits of State Spaces IV. Fractal Label Sets
Lanéry, Suzanne
2015-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [Kijowski 1977] to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier w...
ONLINE MONITORING STEADY STATE STABILITY LIMIT PADA SISTEM INTERKONEKSI SULSELRABAR
2015-01-01
Pada beberapa dekade terakhir, fenomena black-out (pemadaman total)akibat voltage collapse mengalami peningkatan.Hal ini disebabkan oleh peningkatan konsumen pemakai listrik yang tidak sebanding dengan peningkatan pembangkit dan pengembangan jaringan transmisi. Berdasarkan kenyataan dilapangan, ketidakstabilan steady state sangat berhubungan dengan rendahnya ketersediaan daya aktif/reaktif, level tegangan yang rendah, dan besarnya perubahan tegangan untuk perubahan beban atau daya pembangkit....
Limit State of Materials and Structures Direct Methods 2
Oueslati, Abdelbacet; Charkaluk, Eric; Tritsch, Jean-Bernard
2013-01-01
To determine the carrying capacity of a structure or a structural element susceptible to operate beyond the elastic limit is an important task in many situations of both mechanical and civil engineering. The so-called “direct methods” play an increasing role due to the fact that they allow rapid access to the request information in mathematically constructive manners. They embrace Limit Analysis, the most developed approach now widely used, and Shakedown Analysis, a powerful extension to the variable repeated loads potentially more economical than step-by-step inelastic analysis. This book is the outcome of a workshop held at the University of Sciences and Technology of Lille. The individual contributions stem from the areas of new numerical developments rendering these methods more attractive for industrial design, extension of the general methodology to new horizons, probabilistic approaches and concrete technological applications.
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
In this paper a set of sufficient conditions is developed in terms of controllability and observability functions under which a given state-space realization of a formal power series is minimal. Specifically, it is shown that positivity of these functions, in addition to a stability requirement and
Institute of Scientific and Technical Information of China (English)
Su Shi-Lei; Wang Yuan; Guo Qi; Wang Hong-Fu; Zhang Shou
2012-01-01
We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements,cross-Kerr nonlinearity,and homodyne measurement,therefore it is feasible with current experimental technology.The success probability of our protocol is optimal,this property makes our protocol more efficient than others in the applications of quantum communication.
Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Energy Technology Data Exchange (ETDEWEB)
Thingna, Juzar [Institute of Physics, University of Augsburg, Universitätsstrasse 1 D-86135 Augsburg (Germany); Nanosystems Initiative Munich, Schellingrstrasse 4, D-80799 München (Germany); Zhou, Hangbo [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore); NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117456 (Singapore); Wang, Jian-Sheng, E-mail: phywjs@nus.edu.sg [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore)
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Chai, Lin; Qian, Chunjiang
2015-06-01
This paper investigates the design problem of constructing the state and output feedback stabilisation controller for a class of uncertain nonlinear systems subject to time-delay. First, a dynamic linear state feedback control law with an adaptive strategy is developed to globally stabilise the uncertain nonlinear time-delay system under a lower-triangular higher-order growth condition. Then, one more challenging problem of the adaptive output feedback stabilisation is addressed, which can globally stabilise the time-delay system when the unmeasurable states linearly grow with rate functions consisting of higher-order output.
Further limit on 3α decay of Hoyle state
Directory of Open Access Journals (Sweden)
Rana T. K.
2014-03-01
Full Text Available The quantitative contributions of various direct three alpha decay mechanisms in the decay of the famous Hoyle state, the 02+ resonant excited state of 12C at excitation energy of 7.65 MeV, has been estimated using 60 MeV α inelastic scattering on 12C target in complete kinematical measurement. Simultaneous optimisation of three different distributions (the relative energy of 8Be like pairs, the root mean square energy deviation and the radial projection of symmetric Dalitz plot derived from the experimental data with those generated from the Monte Carlo simulated event sets, have been done to arrive at a consistent estimation of the contributions of various direct decay modes.
Quantum States, Thermodynamic Limits and Entropy in M-Theory
Abdalla, Maria Christina B; Guimarães, M E X
2003-01-01
We discuss the matching of the BPS part of the spectrum for (super)membrane, which gives the possibility of getting membrane's results via string calculations. In the small coupling limit of M--theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at large coupling constant is computed by considering M--theory on a manifold with topology ${\\mathbb T}^2\\times{\\mathbb R}^9$. We argue that the finite temperature partition functions (brane Laurent series for $p \
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam; Friis-Hansen, Peter; Jensen, Jørgen Juncher
2009-01-01
Onboard decision support systems (DSS) are used to increase the operational safety of ships. Ideally, DSS can estimate future ship responses within a time scale of the order of 1–3 h taking into account speed and course changes, assuming stationary sea states. In principle, the calculations depend...... on a large amount of operational and environmental parameters, which will be known only in the statistical sense. The present paper suggests a procedure to incorporate random variables and associated uncertainties in the calculations of the outcrossing rates that are the basis for riskbased DSS....... The procedure is based on parallel system analysis, and the paper derives and describes the main ideas. The concept is illustrated by an example, where the limit state of a non-linear ship response is considered. The results from the parallel system analysis are in agreement with corresponding Monte Carlo...
Misawa, Tetsuro; Yokoyama, Takehito; Murakami, Shuichi
2012-02-01
Recent photoelectron spectroscopy experiments have revealed the presence of the Dirac cone on the surface of the topological insulator and its spin-splitting due to the spin-orbit interaction. In general, on spin-orbit coupled systems, electric fields induce spin polarizations as linear and nonlinear responses. Here we investigate the inverse Faraday effect on the surface of the topological insulator. The inverse Faraday effect is a non-linear optical effect where a circularly polarized light induces a dc spin polarization. We employ the Keldysh Green's function method to calculate the induced spin polarization and discuss its frequency dependence. In particular, in the low frequency limit, our analytical result gives the spin polarization proportional to the frequency and the square of the lifetime. As for the finite frequency regime, we employ numerical methods to discuss the resonance due to interband transitions. We also discuss the photogalvanic effect, where an illumination of a circular polarized light generates the dc charge current. Lastly, we evaluate those quantities with realistic parameters.[4pt] [1] T. Misawa, T. Yokoyama, S. Murakami, Phys. Rev. B84, 165407 (2011).
Exotic magnetic states in Pauli-limited superconductors.
Kenzelmann, M
2017-03-01
Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.
Exotic magnetic states in Pauli-limited superconductors
Kenzelmann, M.
2017-03-01
Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.
2011-05-24
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Increase for the Common Pool Fishery...), Commerce. ACTION: Temporary rule; inseason adjustment of trip limit. SUMMARY: NMFS increases the trip limit... Regional Administrator (RA) to adjust the trip limits for common pool vessels in order to optimize the...
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Directory of Open Access Journals (Sweden)
A.M. Elnaggar
2016-01-01
Full Text Available An analysis of primary, superharmonic of order five, and subharmonic of order one-three resonances for non-linear s.d.o.f. system with two distinct time-delays under an external excitation is investigated. The method of multiple scales is used to determine two first order ordinary differential equations which describe the modulation of the amplitudes and the phases. Steady-state solutions and their stabilities in each resonance are studied. Numerical results are obtained by using the Software of Mathematica, which presented in a group of figures. The effect of the feedback gains and time-delays on the non-linear response of the system is discussed and it is found that: an appropriate feedback can enhance the control performance. A suitable choice of the feedback gains and time-delays can enlarge the critical force amplitude, and reduce the peak amplitude of the response (or peak amplitude of the free oscillation term for the case of primary resonance (superharmonic resonance. Furthermore, a proper feedback can eliminate saddle-node bifurcation, thereby eliminating jump and hysteresis phenomena taking place in the corresponding uncontrolled system. For subharmonic resonance, an adequate feedback can reduce the regions of subharmonic resonance response.
Surface Gap Soliton Ground States for the Nonlinear Schr\\"{o}dinger Equation
Dohnal, Tomáš; Reichel, Wolfgang
2010-01-01
We consider the nonlinear Schr\\"{o}dinger equation $(-\\Delta +V(x))u = \\Gamma(x) |u|^{p-1}u$, $x\\in \\R^n$ with $V(x) = V_1(x) \\chi_{\\{x_1>0\\}}(x)+V_2(x) \\chi_{\\{x_10\\}}(x)+\\Gamma_2(x) \\chi_{\\{x_1<0\\}}(x)$ and with $V_1, V_2, \\Gamma_1, \\Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\\min \\sigma(-\\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\\equiv V_1, \\Gamma\\equiv \\Gamma_1$ and $V\\equiv V_2, \\Gamma\\equiv \\Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\\tfrac{d^2}{dx^2} +V_1(x)$ an...
Perspectives for quantum state engineering via high non-linearity in a double-EIT regime
Paternostro, M; Ham, B S
2003-01-01
We analyse the possibilities for quantum state engineering offered by a model for Kerr-type non-linearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [{\\sl Phys. Rev. A} {\\bf 65}, 33833 (2002)]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows ...
Directory of Open Access Journals (Sweden)
Hideki Gotoh
2014-10-01
Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.
Tadepalli, Siva Kumar; Krishna Rao Kandanvli, V.; Kar, Haranath
2015-11-01
A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), 'Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities', International Journal of Systems Science, 42, 397-406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), 'Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach', Signal Processing, 89, 161-173) is recovered from their approach as a special case. It is shown that this claim is not justified.
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1990-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1991-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Identification of climatic state with limited proxy data
Directory of Open Access Journals (Sweden)
J. D. Annan
2012-07-01
Full Text Available We investigate the identifiability of the climate by limited proxy data. We test a data assimilation approach through perfect model pseudoproxy experiments, using a simple likelihood-based weighting based on the particle filtering process. Our experimental set-up enables us to create a massive 10 000-member ensemble at modest computational cost, thus enabling us to generate statistically robust results. We find that the method works well when data are sparse and imprecise, but in this case the reconstruction has a rather low accuracy as indicated by residual RMS errors. Conversely, when data are relatively plentiful and accurate, the estimate tracks the target closely, at least when considering the hemispheric mean. However, in this case, our prior ensemble size of 10 000 appears to be inadequate to correctly represent the true posterior, and the regional performance is poor. Using correlations to assess performance gives a more encouraging picture, with significant correlations ranging from about 0.3 when data are sparse to values over 0.7 when data are plentiful, but the residual RMS errors are substantial in all cases. Our results imply that caution is required in interpreting climate reconstructions, especially when considering the regional scale, as skill on this basis is markedly lower than on the large scale of hemispheric mean temperature.
THE LIMITS OF STATE POWER IN A DEMOCRATIC SOCIETY
Directory of Open Access Journals (Sweden)
Marius ANDREESCU
2016-05-01
Full Text Available The coding is not only the expression of the political will of the law maker, it firstly is a complex juridical technique for the choosing and systematization of the normative content necessary and adequate to certain social, political, economic, institutional realities. Since Constitution is a law, yet it nevertheless distinguishes itself from the law, the problem is to establish which juridical norms it contains. The solving of this problem needs to consider the specific of the fundamental law and also of the requirements of the coding theory. The determining with all scientific stringency of the normative content of the Constitution is indispensible both for the removal of any inaccuracy in delimiting the differences from the law, for the stability and predictability of the fundamental law and last, but not the least, for the reality and effectiveness of its supremacy. In our study we realize an analysis based on compared criterions of the techniques and exigencies for the choosing and systematization of the constitutional norms with reference to their specific, to the practice of other states and within a historical context. The analysis is aiming to the actual proposals for the revising of the Constitution.
Limiting net greenhouse gas emissions in the United States
Energy Technology Data Exchange (ETDEWEB)
Bradley, R A; Watts, E C; Williams, E R [eds.
1991-09-01
In 1988, Congress requested that DOE produce a study on carbon dioxide inventory and policy to provide an inventory of emissions sources and to analyze policies to achieve a 20% reduction in carbon dioxide emissions in 5 to 10 years and a 50% reduction in 15 to 20 years. Energy and environmental technology data were analyzed using computational analysis models. This information was then evaluated, drawing on current scientific understanding of global climate change, the possible consequences of anthropogenic climate change (change caused by human activity) and the relationship between energy production and use and the emission of radiatively important gases. Topics discussed include: state of the science in estimating atmosphere/climate change relationships, the potential consequences of atmosphere/climate change, us greenhouse emissions past and present, an approach to analyzing the technical potential and cost of reducing US energy-related greenhouse gas emissions, current policy base and National Energy Strategy actions, fiscal instruments, regulatory instruments, combined strategies and instruments, macroeconomic impacts, carbon taxation and international trade, a comparison to other studies.
Transient and Steady-State Analysis of Nonlinear RF and Microwave Circuits
Directory of Open Access Journals (Sweden)
Zhu Lei(Lana
2006-01-01
Full Text Available This paper offers a review of simulation methods currently available for the transient and steady-state analysis of nonlinear RF and microwave circuits. The most general method continues to be the time-marching approach used in Spice, but more recent methods based on multiple time dimensions are particularly effective for RF and microwave circuits. We derive nodal formulations for the most widely used multiple time dimension methods. We put special emphasis on methods for the analysis of oscillators based in the warped multitime partial differential equations (WaMPDE approach. Case studies of a Colpitts oscillator and a voltage controlled Clapp-Gouriet oscillator are presented and discussed. The accuracy of the amplitude and phase of these methods is investigated. It is shown that the exploitation of frequency-domain latency reduces the computational effort.
Periodicity in a Nonlinear Predator-prey System with State Dependent Delays
Institute of Scientific and Technical Information of China (English)
Feng-de Chen; Jin-lin Shi
2005-01-01
With the help of a continuation theorem based on Gainesand Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system{dN1(t)/dt=N1(t)[b1(t)-n∑i=1 ai(t)(N1(t-Ti(t,N1(t), N2(t))))ai-m∑cj(t)(N2(t-σj(t,Ni(t),N2(t))))βj],dN2(t)/dt=N2(t)[b2(t)-n∑i=1 di(t)(N1(t-Pi(t,N1(t), N2(t))))γi],where ai (t), cj (t), di(t) are continuous positive periodic functions with periodic ω＞ 0, b1 (t), b2 (t) are continuousare positive constants.
Lewis, Robert Michael
1997-01-01
This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
Optical diode action from axially asymmetric nonlinearity in an all-carbon solid-state device.
Anand, Benoy; Podila, Ramakrishna; Lingam, Kiran; Krishnan, S R; Siva Sankara Sai, S; Philip, Reji; Rao, Apparao M
2013-01-01
Nanostructured carbons are posited to offer an alternative to silicon and lead to further miniaturization of photonic and electronic devices. Here, we report the experimental realization of the first all-carbon solid-state optical diode that is based on axially asymmetric nonlinear absorption in a thin saturable absorber (graphene) and a thin reverse saturable absorber (C60) arranged in tandem. This all-optical diode action is polarization independent and has no phase-matching constraints. The nonreciprocity factor of the device can be tuned by varying the number of graphene layers and the concentration or thickness of the C60 coating. This ultracompact graphene/C60 based optical diode is versatile with an inherently large bandwidth, chemical and thermal stability, and is poised for cost-effective large-scale integration with existing fabrication technologies.
Electric vehicle state of charge estimation: Nonlinear correlation and fuzzy support vector machine
Sheng, Hanmin; Xiao, Jian
2015-05-01
The aim of this study is to estimate the state of charge (SOC) of the lithium iron phosphate (LiFePO4) battery pack by applying machine learning strategy. To reduce the noise sensitive issue of common machine learning strategies, a kind of SOC estimation method based on fuzzy least square support vector machine is proposed. By applying fuzzy inference and nonlinear correlation measurement, the effects of the samples with low confidence can be reduced. Further, a new approach for determining the error interval of regression results is proposed to avoid the control system malfunction. Tests are carried out on modified COMS electric vehicles, with two battery packs each consists of 24 50 Ah LiFePO4 batteries. The effectiveness of the method is proven by the test and the comparison with other popular methods.
Signatures of nonlinear optomechanics and engineering of nonclassical mechanical steady states
Borkje, Kjetil
2013-03-01
Motivated by recent improvements in coupling strength between light and mechanical motion, we study the strong coupling regime of cavity optomechanics theoretically. We focus on the regime where the optomechanical coupling rate is still small compared to the mechanical resonance frequency, but where the mechanically induced Kerr nonlinearity is significant. The response of the system to an optical drive is characterized. The average photon number in the cavity as a function of drive detuning can feature several peaks due to multi-photon transitions. Furthermore, we show that by optically driving the system at multiple frequencies, multi-photon transitions can facilitate the engineering of nonclassical steady states of the mechanical oscillator. The author acknowledges financial support from The Danish Council for Independent Research under the Sapere Aude program.
Mani, Kamal P.; Sreekanth, Perumbilavil; Vimal, G.; Biju, P. R.; Unnikrishnan, N. V.; Ittyachen, M. A.; Philip, Reji; Joseph, Cyriac
2016-12-01
Photoluminescence properties and optical limiting behavior of pure and Sm3+/Eu3+ doped Tb2(MoO4)3 nanophosphors are investigated. The prepared nanophosphors exhibit excellent emission when excited by UV light. Color-tunable emissions in Tb2-xSmx(MoO4)3 and Tb2-xEux(MoO4)3 are realized by employing different excitation wavelengths or by controlling the doping concentration of Sm3+ and Eu3+. Luminescence quantum yield and CIE chromatic coordinates of the prepared phosphors were also presented. Optical limiting properties of the samples are investigated by open aperture Z-scan technique using 5 ns laser pulses at 532 nm. Numerical fitting of the measured Z-scan data to the relevant nonlinear transmission equations reveals that the nonlinear absorption is arising from strong excited state absorption, along with weak absorption saturation and it is found that the optical nonlinearity of Tb2(MoO4)3 increases with Sm3+/Eu3+doping. Parameters such as saturation fluence, excited state absorption cross section and ground state absorption cross section of the samples have been determined numerically, from which the figure of merit for nonlinear absorption is calculated. The excited state absorption cross-section of the samples is found to be one order of magnitude higher than that of the ground state absorption cross-section, indicating strong reverse saturable absorption. These results indicate that Sm3+/Eu3+ doped Tb2(MoO4)3 nanophosphors are efficient media for UV/n-UV pumped LEDs, and are also potential candidates for designing efficient optical limiting devices for the protection of human eyes and sensitive optical detectors from harmful laser radiation.
State Anxiety and Nonlinear Dynamics of Heart Rate Variability in Students
Dimitriev, Aleksey D.
2016-01-01
Objectives Clinical and experimental research studies have demonstrated that the emotional experience of anxiety impairs heart rate variability (HRV) in humans. The present study investigated whether changes in state anxiety (SA) can also modulate nonlinear dynamics of heart rate. Methods A group of 96 students volunteered to participate in the study. For each student, two 5-minute recordings of beat intervals (RR) were performed: one during a rest period and one just before a university examination, which was assumed to be a real-life stressor. Nonlinear analysis of HRV was performed. The Spielberger’s State-Trait Anxiety Inventory was used to assess the level of SA. Results Before adjusting for heart rate, a Wilcoxon matched pairs test showed significant decreases in Poincaré plot measures, entropy, largest Lyapunov exponent (LLE), and pointwise correlation dimension (PD2), and an increase in the short-term fractal-like scaling exponent of detrended fluctuation analysis (α1) during the exam session, compared with the rest period. A Pearson analysis indicated significant negative correlations between the dynamics of SA and Poincaré plot axes ratio (SD1/SD2), and between changes in SA and changes in entropy measures. A strong negative correlation was found between the dynamics of SA and LLE. A significant positive correlation was found between the dynamics of SA and α1. The decreases in Poincaré plot measures (SD1, complex correlation measure), entropy measures, and LLE were still significant after adjusting for heart rate. Corrected α1 was increased during the exam session. As before, the dynamics of adjusted LLE was significantly correlated with the dynamics of SA. Conclusions The qualitative increase in SA during academic examination was related to the decrease in the complexity and size of the Poincaré plot through a reduction of both the interbeat interval and its variation. PMID:26807793
State Anxiety and Nonlinear Dynamics of Heart Rate Variability in Students.
Directory of Open Access Journals (Sweden)
Dimitriy A Dimitriev
Full Text Available Clinical and experimental research studies have demonstrated that the emotional experience of anxiety impairs heart rate variability (HRV in humans. The present study investigated whether changes in state anxiety (SA can also modulate nonlinear dynamics of heart rate.A group of 96 students volunteered to participate in the study. For each student, two 5-minute recordings of beat intervals (RR were performed: one during a rest period and one just before a university examination, which was assumed to be a real-life stressor. Nonlinear analysis of HRV was performed. The Spielberger's State-Trait Anxiety Inventory was used to assess the level of SA.Before adjusting for heart rate, a Wilcoxon matched pairs test showed significant decreases in Poincaré plot measures, entropy, largest Lyapunov exponent (LLE, and pointwise correlation dimension (PD2, and an increase in the short-term fractal-like scaling exponent of detrended fluctuation analysis (α1 during the exam session, compared with the rest period. A Pearson analysis indicated significant negative correlations between the dynamics of SA and Poincaré plot axes ratio (SD1/SD2, and between changes in SA and changes in entropy measures. A strong negative correlation was found between the dynamics of SA and LLE. A significant positive correlation was found between the dynamics of SA and α1. The decreases in Poincaré plot measures (SD1, complex correlation measure, entropy measures, and LLE were still significant after adjusting for heart rate. Corrected α1 was increased during the exam session. As before, the dynamics of adjusted LLE was significantly correlated with the dynamics of SA.The qualitative increase in SA during academic examination was related to the decrease in the complexity and size of the Poincaré plot through a reduction of both the interbeat interval and its variation.
Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems
Institute of Scientific and Technical Information of China (English)
Wu Ligang; Wang Changhong; Gao Huijun; Zhang Lixian
2006-01-01
A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.
Institute of Scientific and Technical Information of China (English)
Shu-hai ZHANG; Xiao-gang DENG; Mei-liang MAO; Chi-Wang SHU
2013-01-01
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X.and Zhang H.(2000),J.Comput.Phys.165,22-44 and Zhang S.,Jiang S.and Shu C.-W.(2008),J.Comput.Phys.227,7294-7321] is studied through numerical tests.Like most other shock capturing schemes,WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level.In this paper,the techniques studied in [Zhang S.and Shu.C.-W.(2007),J.Sci.Comput.31,273-305 and Zhang S.,Jiang S and Shu.C.-W.(2011),J.Sci.Comput.47,216-238],to improve the convergence to steady state solutions for WENO schemes,are generalized to the WCNS.Detailed numerical studies in one and two dimensional cases are performed.Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS.The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.
Zhang, Xing; Mu, Mu; Wang, Qiang; Pierini, Stefano
2017-06-01
In this study, the initial perturbations that are the easiest to trigger the Kuroshio Extension (KE) transition connecting a basic weak jet state and a strong, fairly stable meandering state, are investigated using a reduced-gravity shallow water ocean model and the CNOP (Conditional Nonlinear Optimal Perturbation) approach. This kind of initial perturbation is called an optimal precursor (OPR). The spatial structures and evolutionary processes of the OPRs are analyzed in detail. The results show that most of the OPRs are in the form of negative sea surface height (SSH) anomalies mainly located in a narrow band region south of the KE jet, in basic agreement with altimetric observations. These negative SSH anomalies reduce the meridional SSH gradient within the KE, thus weakening the strength of the jet. The KE jet then becomes more convoluted, with a high-frequency and large-amplitude variability corresponding to a high eddy kinetic energy level; this gradually strengthens the KE jet through an inverse energy cascade. Eventually, the KE reaches a high-energy state characterized by two well defined and fairly stable anticyclonic meanders. Moreover, sensitivity experiments indicate that the spatial structures of the OPRs are not sensitive to the model parameters and to the optimization times used in the analysis.
Sudheesh, P.; Siji Narendran, N. K.; Chandrasekharan, K.
2013-12-01
Here we report a study on the third-order nonlinear optical properties of a new class of phenylhydrazones and the influence of silver and gold metal nanoparticles on their nonlinear response. Metal nanoparticles were prepared by laser ablation method. Single beam Z-scan technique with a 7 ns, 10 Hz Nd: YAG laser pulses at 532 nm were employed for the measurements. The compounds exhibit well optical limiting properties. Hence, these compounds are a promising class of materials for the optical device applications.
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2002-01-01
of reinforced concrete slabs or the stability of slopes, and generally, whenever all information about the structure, except for the ultimate magnitude of the load set, is known. However, in the design of structures the situation is the opposite. Here the loads are known whereas the necessary dimensions...
Strong third-order nonlinear response and optical limiting of α-NiMoO4 nanoparticles
Das, Amlan; Ratha, Satyajit; Yadav, Rajesh Kumar; Mondal, Anirban; Rout, Chandra Sekhar; Adarsh, K. V.
2017-07-01
In this manuscript, we demonstrate the strong resonant two photon absorption coefficient ≈71 ± 5 cm/GW at 532 nm in α-NiMoO4 nanoparticles prepared by a facile hydrothermal method. Strikingly, we have obtained the optical limiting onset threshold fluence (FON) of 36 mJ/cm2 for the linear transmittance of 0.64 with an excellent two photon absorption cross section (38 × 10-45 cm4 s), which suggests that they can be utilized as passive optical limiters. To explain the observed effects, we present a two-level rate equation model and numerically simulated the Z-scan peak shape, which is in good agreement with the experimental data. Further, we also show the normalized population density of the carriers in excited and ground states.
Tao, Jili; Ma, Longhua; Zhu, Yong
2016-11-01
Inspired by the state space model based predictive control, this paper presents the combination design of extended non-minimal state space predictive control (ENMSSPC) and modified linear quadratic regulator (LQR) for a kind of nonlinear process with output feedback coupling, which shows improved control performance for both model/plant match and model/plant mismatch cases. In many previous control methods for this kind of nonlinear systems, the nonlinear part is treated in different ways such as ignored, represented as a rough linear one or assumed to be time-variant when corresponding predictive control methods are designed. However, the above methods will generally lead to information loss, resulting in the influenced control performance. This paper will show that the ENMSSPC-LQ control structure will further improve closed-loop control performance concerning tracking ability and disturbance rejection compared with previous predictive control methods.
Chang, Wen-Jer; Huang, Bo-Jyun
2014-11-01
The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.
Fuzzy analysis of serviceability limit state of slender steel beam under bending
Energy Technology Data Exchange (ETDEWEB)
Kala, Zdeněk; Valeš, Jan [Brno University of Technology, Faculty of Civil Engineering, Department of Structural Mechanics Vevefi St. 95, ZIP 602 00, Brno (Czech Republic)
2015-03-10
In the present paper, deformations of a beam under equal end moments solved with influence of lateral buckling are studied. It has been found by numerical studies that the lateral deflection of slender beam under major axis bending can be relatively high.The acceptability of high values of lateral deflections within the framework of serviceability limit state is discussed. In the next part of the paper, the limit value of maximum deflection was introduced as a fuzzy number. The fuzzy analysis of the maximum moment which causes the maximum deflection was carried out. The slendernesses of beams for which the serviceability limit state is the limiting state for design were identified.
Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.
2017-03-01
Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
Pathak, A
2006-01-01
Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.
Edelaar, Lisa M; van Dieën, Jaap H; van der Esch, Martin; Roorda, Leo D; Dekker, Joost; Lems, Willem F; van der Leeden, Marike
2017-07-07
To investigate whether relationships between upper leg muscle strength and activity limitations are non-linear in patients with knee osteoarthritis, and, if so, to determine muscle strength thresholds for limitations in daily activities. Baseline data were used for 562 patients with knee osteoarthritis in the Amsterdam-Osteoarthritis cohort. Upper leg muscle strength (Nm/kg) was measured isokinetically. Activity limitations were measured with the timed Get Up and Go test and timed Stair Climb Test, subdivided into stair-ascent and stair-descent. Linear and non-linear relationships between muscle strength and activity limitations were evaluated, and thresholds were determined. Non-linear models improved model fit compared with linear models. The improvement in percentage variance accounted for was 5.9, 8.2 and 5.2 percentage points for the timed Get Up and Go, stair-ascent and stair-descent times, respectively. Muscle strength thresholds were 0.93 Nm/kg (95% confidence interval (95% CI) 0.82-1.04), 0.89 Nm/kg (95% CI 0.77-1.02) and 0.97 Nm/kg (95% CI 0.85-1.11) for relationships with timed Get Up and Go, stair-ascent and stair-descent times, respectively. In patients with knee osteoarthritis, relationships between muscle strength and activity limitations are non-linear. Patients with muscle strength below the described thresholds might benefit more from muscle strength training to reduce limitations in daily activities than would patients with muscle strength above the thresholds. Further research is needed to assess the clinical value of the thresholds determined.
2011-10-20
... States; Highly Migratory Species Fisheries; Swordfish Retention Limits AGENCY: National Marine Fisheries... and Management Act (MSA) to modify retention limits for swordfish, Xiphias gladius, harvested in the U... FMP regulations governing the possession and landing limits of swordfish captured in the DSLL...
2012-03-19
... States; Highly Migratory Species Fisheries; Swordfish Retention Limits AGENCY: National Marine Fisheries...) to modify retention limits for swordfish harvested in the U.S. West Coast-based deep-set tuna... limits of swordfish captured in the DSLL fishery as follows: if a vessel without an observer onboard...
2013-11-04
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustments for the Common Pool Fishery... Handgear A, Handgear B, and Small Vessel Category permits be adjusted relative to the cod trip limits for DAS vessels, and these adjustments are specified in Table 3. These trip limit adjustments for all...
2013-02-14
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustments for the Common Pool Fishery... fishing year. This rule also decreases the trip limits for white hake and pollock. This is intended to...) established the current trip limits for the common pool vessels fishing under a Category A day-at-sea (DAS...
2011-04-05
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustments for the Common Pool Fishery... Southern New England (SNE)/Mid-Atlantic (MA) yellowtail flounder, and reduces the trip limit GOM cod and... additional overharvest of these stocks relative to the pertinent common pool sub-ACLs. DATES: The trip limit...
2010-07-30
... States; Northeast Multispecies Fishery; Trip Limit Reduction and Trawl Gear Restriction AGENCY: National..., Northeast (NE) Region, NMFS (Regional Administrator) to increase or decrease the trip limits for vessels in... common pool sub-ACL prior to April 30, 2011, would require drastic trip limit reductions and/or...
2013-09-03
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustments for the Common Pool Fishery... percent of its Gulf of Maine (GOM) haddock allocation of 2 mt. Despite a trip limit reduction for SNE/MA... overharvest, the trip limit for SNE/MA winter flounder is reduced to 300 lb (136.1 kg) per trip, and the GOM...
2013-07-16
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustment for the Common Pool Fishery... winter flounder and GOM haddock. DATES: The trip limit decrease for SNE/MA winter flounder is effective... of 136 mt (299,829 lb). The current trip limit for SNE/MA winter flounder is 5,000 lb (2,268 kg) per...
Limited Out-of-State Data Needed to Produce Robust Indicators. Breaking down State Silos
Data Quality Campaign, 2012
2012-01-01
There is increasing demand on the education sector to produce high-quality, actionable information to inform decisions aimed at improving student achievement. Unfortunately, every state currently lacks the out-of-state data necessary to follow individuals systemically and efficiently across state lines. The absence of appropriate out-of-state data…
Directory of Open Access Journals (Sweden)
Hongjian Wang
2014-01-01
Full Text Available We present a support vector regression-based adaptive divided difference filter (SVRADDF algorithm for improving the low state estimation accuracy of nonlinear systems, which are typically affected by large initial estimation errors and imprecise prior knowledge of process and measurement noises. The derivative-free SVRADDF algorithm is significantly simpler to compute than other methods and is implemented using only functional evaluations. The SVRADDF algorithm involves the use of the theoretical and actual covariance of the innovation sequence. Support vector regression (SVR is employed to generate the adaptive factor to tune the noise covariance at each sampling instant when the measurement update step executes, which improves the algorithm’s robustness. The performance of the proposed algorithm is evaluated by estimating states for (i an underwater nonmaneuvering target bearing-only tracking system and (ii maneuvering target bearing-only tracking in an air-traffic control system. The simulation results show that the proposed SVRADDF algorithm exhibits better performance when compared with a traditional DDF algorithm.
Steady-state probability density function in wave turbulence under large volume limit
Institute of Scientific and Technical Information of China (English)
Yeontaek Choia; Sang Gyu Job
2011-01-01
We investigate the possibility for two-mode probability density function (PDF) to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state two- or higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.
Zitelli, Gregory; Djouadi, Seddik M; Day, Judy D
2015-10-01
The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.
Anand, Benoy; Molli, Muralikrishna; Aditha, Saikiran; Mimani Rattan, Tanu; Siva Sankara Sai, S.; Kamisetti, Venkataramaniah
2013-09-01
Transition metal selenides (FeSe2 and Cu2Se) are synthesized by the hydrothermal co-reduction method. XRD results revealed the crystalline nature of their single phase and the elemental compositions are obtained using EDS. TEM images of the as-prepared samples show the formation of nanorods of 10-20 nm diameter in case of iron selenide and nanoparticles of 10-35 nm diameter in case of copper selenide. The energy bandgap values are calculated using tauc plots obtained from UV-Visible absorption spectra. The open aperture Z-scan measurements carried out using 5 ns pulses at 532 nm revealed that the samples showed excellent optical limiting behavior owing to strong nonlinear absorption (NLA). Through numerical simulations, the mechanism of NLA is found to be effective three-photon absorption which has significant contribution from excited state absorption.
Li, Huiping; Shi, Yang
2012-10-01
This article focuses on the state-feedback ℋ∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton-Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ℋ∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ℋ∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
Soliton states of Maxwell’s equations and nonlinear Schrodinger equation
Institute of Scientific and Technical Information of China (English)
陈翼强
1997-01-01
Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrodinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed.It is found that in some cases,the soliton solutions to the nonlinear Schrodinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrodinger equation through approximation,although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference.The origin of the differences is also discussed.
Institute of Scientific and Technical Information of China (English)
Gongming WEI
2008-01-01
A 2-coupled nonlinear Schr(o)dinger equations with bounded varying potentials and strongly attractive interactions is considered.When the attractive interaction is strong enough,the existence of a ground state for sufficiently small Planck constant is proved.As the Planck constant approaches zero,it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.
Institute of Scientific and Technical Information of China (English)
Shu-jun Liu; Ji-feng Zhang; Zhong-ping Jiang
2008-01-01
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical)stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
Larsen, Jon S.; Santos, Ilmar F.
2015-06-01
The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.
Bartels, Robert E.
2002-01-01
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
Directory of Open Access Journals (Sweden)
Dalei Song
2012-10-01
Full Text Available The adaptive extended set‐membership filter (AESMF for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method‐based adaptive set‐membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed MIT‐AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.
Ding, Derui; Wang, Zidong; Hu, Jun; Shu, Huisheng
2013-04-01
In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.
Energy Technology Data Exchange (ETDEWEB)
Kwon, Younghun, E-mail: yyhkwon@hanyang.ac.kr
2015-09-02
In this article, we investigate the nonlocal behavior of the quantum state of fermionic system having the alpha vacuum. We evaluate the maximum violation of CHSH inequality in the quantum state. Even when the maximally entangled quantum state is initially shared it cannot violate the CHSH inequality, regardless of any alpha vacuum, when the infinite acceleration is applied. It means that the nonlocality of the quantum state in fermionic system with the alpha vacuum cannot survive in the infinite acceleration limit.
Castaños, Octavio; Schuch, Dieter; Rosas-Ortiz, Oscar
2013-02-01
Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases, the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfils a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.
Solid-State Radio Frequency Plasma Heating Using a Nonlinear Transmission Line
Miller, Kenneth; Ziemba, Timothy; Prager, James; Slobodov, Ilia
2015-11-01
Radio Frequency heating systems are rarely used by the small-scale validation platform experiments due to the high cost and complexity of these systems, which typically require high power gyrotrons or klystrons, associated power supplies, waveguides and vacuum systems. The cost and complexity of these systems can potentially be reduced with a nonlinear transmission line (NLTL) based system. In the past, NLTLs have lacked a high voltage driver that could produce long duration high voltage pulses with fast rise times at high pulse repetition frequency. Eagle Harbor Technologies, Inc. (EHT) has created new high voltage nanosecond pulser, which combined with NLTL technology will produce a low-cost, fully solid-state architecture for the generation of the RF frequencies (0.5 to 10 GHz) and peak power levels (~ 10 MW) necessary for plasma heating and diagnostic systems for the validation platform experiments within the fusion science community. The proposed system does not require the use of vacuum tube technology, is inherently lower cost, and is more robust than traditional high power RF heating schemes. Design details and initial bench testing results for the new RF system will be presented. This work is supported under DOE Grant # DE-SC0013747.
Wen, Guoguang; Yu, Yongguang; Peng, Zhaoxia; Rahmani, Ahmed
2016-06-01
This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.
Directory of Open Access Journals (Sweden)
Wameedh Riyadh Abdul-Adheem
2016-12-01
Full Text Available This paper presents a new strategy for the active disturbance rejection control (ADRC of a general uncertain system with unknown bounded disturbance based on a nonlinear sliding mode extended state observer (SMESO. Firstly, a nonlinear extended state observer is synthesized using sliding mode technique for a general uncertain system assuming asymptotic stability. Then the convergence characteristics of the estimation error are analyzed by Lyapunov strategy. It revealed that the proposed SMESO is asymptotically stable and accurately estimates the states of the system in addition to estimating the total disturbance. Then, an ADRC is implemented by using a nonlinear state error feedback (NLSEF controller; that is suggested by J. Han and the proposed SMESO to control and actively reject the total disturbance of a permanent magnet DC (PMDC motor. These disturbances caused by the unknown exogenous disturbances and the matched uncertainties of the controlled model. The proposed SMESO is compared with the linear extended state observer (LESO. Through digital simulations using MATLAB / SIMULINK, the chattering phenomenon has been reduced dramatically on the control input channel compared to LESO. Finally, the closed-loop system exhibits a high immunity to torque disturbance and quite robustness to matched uncertainties in the system.
Sarkar, Resham
In this thesis, we show first how to formulate the properties of all the collective states under various non-idealities, and use this formulation to understand the dynamics thereof. We show that the collective states corresponding to the absorption of a given number of photons can be visualized as an abstract, multi-dimensional rotation in the Hilbert space spanned by the ordered product states of individual atoms. We also consider the effect of treating the center of mass degree of freedom of the atoms quantum mechanically on the description of the collective states. In particular, we show that it is indeed possible to construct a generalized collective state, as needed for the COSAIN, when each atom is assumed to be in a localized wave packet. (Abstract shortened by ProQuest.).
Bretheim, Joel U; Gayme, Dennice F
2014-01-01
Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a logarithmic region is observed, its von-K\\'arm\\'an constant is not consistent with the standard logarithmic law. In half-channel flow we show that limiting the streamwise-varying wavenumber support of RNL turbulence to one or few empirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNL model follow standard logarithmic behavior for the higher Reynolds numbers in this study.
Heisenberg-limited quantum sensing and metrology with superpositions of twin-Fock states
Gerry, Christopher C.; Mimih, Jihane
2011-03-01
We discuss the prospects of performing Heisenberg-limited quantum sensing and metrology using a Mach-Zehnder interferometer with input states that are superpositions of twin-Fock states and where photon number parity measurements are made on one of the output beams of the interferometer. This study is motivated by the experimental challenge of producing twin-Fock states on opposite sides of a beam splitter. We focus on the use of the so-called pair coherent states for this purpose and discuss a possible mechanism for generating them. We also discuss the prospect of using other superstitions of twin-Fock states, for the purpose of interferometry.
Ionic two photon states and optical nonlinearity in. pi. -conjugated polymers
Energy Technology Data Exchange (ETDEWEB)
Dixit, S.N. (Lawrence Livermore National Lab., CA (USA)); Guo, D.; Mazumdar, S. (Arizona Univ., Tucson, AZ (USA). Dept. of Physics)
1990-11-06
A microscopic mechanism of optical nonlinearity in {pi}-conjugated polymers is presented. It is shown that the bulk of the nonlinearity is determined by only two well defined channels, even though an infinite number of channels are possible in principle. The above conclusion is true for both short and long range Coulomb interactions. The complete frequency dependence of the third harmonic generation in both trans-polyacetylene and polydiacetylene are explained within the same theoretical picture. 19 refs., 4 figs.
Dmitriev, Mikhail G.; Makarov, Dmitry A.
2016-08-01
We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.
Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states
Haw, Jing Yan; Zhao, Jie; Dias, Josephine; Assad, Syed M.; Bradshaw, Mark; Blandino, Rémi; Symul, Thomas; Ralph, Timothy C.; Lam, Ping Koy
2016-10-01
The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound to the quality of the generated clones. However, this limit can be circumvented by abandoning determinism and using probabilistic methods. Here, we report an experimental demonstration of probabilistic cloning of arbitrary coherent states that clearly surpasses the no-cloning limit. Our scheme is based on a hybrid linear amplifier that combines an ideal deterministic linear amplifier with a heralded measurement-based noiseless amplifier. We demonstrate the production of up to five clones with the fidelity of each clone clearly exceeding the corresponding no-cloning limit. Moreover, since successful cloning events are heralded, our scheme has the potential to be adopted in quantum repeater, teleportation and computing applications.
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Phase sensitivity of two nonlinear interferometers with inputting entangled coherent states
Wei, Chao-Ping; Xiao-Yu, Hu; Ya-Fei, Yu; Zhi-Ming, Zhang
2016-04-01
We investigate the phase sensitivity of the SU(1,1) interfereometer [SU(1,1)I] and the modified Mach-Zehnder interferometer (MMZI) with the entangled coherent states (ECS) as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU(1,1)I can beat the shot-noise limit (SNL) and approach the Heisenberg limit (HL). In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU(1,1)I, and the MMZI is more robust against internal photon losses than the SU(1,1)I. Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023), the National Natural Science Foundation of China (Grant Nos. 11574092, 61378012, and 60978009), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20124407110009), the National Basic Research Program of China (Grant Nos. 2011CBA00200 and 2013CB921804), and the Program for Innovative Research Team in University (Grant No. IRT1243).
Zeng, Nianyin; Wang, Zidong; Li, Yurong; Du, Min; Liu, Xiaohui
2011-07-01
In this paper, a mathematical model for sandwich-type lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extended Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also for inspecting the effects from various design parameters in both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes in the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize, and design the properties of lateral flow immunoassay devices. © 2011 IEEE
Quach, Minh; Brunel, Nicolas; d'Alché-Buc, Florence
2007-12-01
Statistical inference of biological networks such as gene regulatory networks, signaling pathways and metabolic networks can contribute to build a picture of complex interactions that take place in the cell. However, biological systems considered as dynamical, non-linear and generally partially observed processes may be difficult to estimate even if the structure of interactions is given. Using the same approach as Sitz et al. proposed in another context, we derive non-linear state-space models from ODEs describing biological networks. In this framework, we apply Unscented Kalman Filtering (UKF) to the estimation of both parameters and hidden variables of non-linear state-space models. We instantiate the method on a transcriptional regulatory model based on Hill kinetics and a signaling pathway model based on mass action kinetics. We successfully use synthetic data and experimental data to test our approach. This approach covers a large set of biological networks models and gives rise to simple and fast estimation algorithms. Moreover, the Bayesian tool used here directly provides uncertainty estimates on parameters and hidden states. Let us also emphasize that it can be coupled with structure inference methods used in Graphical Probabilistic Models. Matlab code available on demand.
Directory of Open Access Journals (Sweden)
Jing Lei
2013-01-01
Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
Poddubny, Alexander N.; Sukhorukov, Andrey A.
2015-09-01
The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, ar
Tremlett, A. J.; Assadian, F.; Purdy, D. J.; Vaughan, N.; Moore, A. P.; Halley, M.
2014-11-01
In the motorsport environment, passive limited slip differentials are a well-established means of improving the traction limitation imposed by the open differential. Torque sensing types are highly adjustable, and can alter both the stability and agility of the vehicle in the various cornering phases of a typical manoeuvre. In this paper, an adjustable clutch plate or 'Salisbury' differential model is presented, which can significantly alter its torque bias characteristics through adjustments in the drive/coast ramp angle, the number of friction faces and preload. To allow robust evaluation of differential parameter changes on ultimate vehicle performance and handling balance, a unified acceleration or 'GG' diagram framework is then described. This builds on traditional GG diagram approaches, by using nonlinear constrained optimisation to define both the vehicle acceleration limits and a 'feasibility' region within the performance envelope. By linearising a seven degrees of freedom vehicle model at multiple operating points, eigenvalue and yaw rate response analysis is then used to establish contours of stability and agility throughout the GG envelope. This brings new insights into the way in which handling balance changes below and up to the vehicle's acceleration limits.
Full-Order Sliding Mode Control for High-Order Nonlinear System Based on Extended State Observer
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; TAO Liang; NAN Yurong
2016-01-01
In this paper,a full-order sliding mode control based on extended state observer (FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer (ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control.Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.
Adaptive control for a class of nonlinear systems with time-varying delays in state and input
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) an...
Wang, Mei-Yu; Yan, Feng-Li; Gao, Ting
2016-07-01
We present two deterministic quantum entanglement distribution protocols for a four-photon Dicke polarization entangled state resorting to the frequency and spatial degrees of freedom, which are immune to an arbitrary collective-noise channel. Both of the protocols adopt the X homodyne measurement based on the cross-Kerr nonlinearity to complete the task of the single-photon detection with nearly unit probability in principle. After the four receivers share the photons, they add some local unitary operations to obtain a standard four-photon Dicke polarization entangled state.
Gao, Fangzheng; Wu, Yuqiang
2015-03-01
This paper considers the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. Comparing with the existing relevant literature, the systems under investigation allow more uncertainties, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state feedback controller is successfully constructed to preserve the equilibrium at the origin and guarantee the global asymptotic stability of the resulting closed-loop system. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.
A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis
Chillara, Vamshi Krishna
2016-01-01
We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions - one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measura...
Schweizer, Kenneth S.; Sussman, Daniel M.
2016-12-01
We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
Stationary states of the two-dimensional nonlinear Schrödinger model with disorder
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth
1998-01-01
Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discr......Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...
The ultimate limit state of the underground circular tunnel segment lining
Ráček, Václav; Zlámal, Jaromír
2017-09-01
Circular tunnel segment lining with staggered joints in track tunnels of Prague Underground was found to be on the ultimate limit state; static analysis (mathematical modeling) is used to determine the causes which led to such situation. This situation is signalized by cracks and related deformations; lining load-limit coefficient can be used to determine the cause. Analysis is performed in the form of parametric study, where the variables are the values of geotechnical figures, the rigidity of the lining with staggered joints and the load of the lining. This paper focuses on analysis of reinforced concrete segmental lining Ø5.3 / 5.8 m (5 + 1 element) and cast iron Ø5.1 / 5.5 m (9 + 1 element). Parametric study using coefficient of loading limit for both of these cases in the Prague Underground leads to fast and relatively easy determination of the cause of the reaching of the ultimate limit state.
Prevalence and impact of dementia-related functional limitations in the United States, 2001 to 2005.
Arrighi, Henry Michael; McLaughlin, Trent; Leibman, Christopher
2010-01-01
These analyses examined the relationship between dementia and comorbid conditions with respect to degree of functional impairment and emotional impact. Analyses were conducted using National Health Interview Survey (2001 through 2005) data from a subset of individuals aged > or =60 years with activity limitations attributed to dementia, senility, or Alzheimer disease compared with those whose limitations were attributed to other conditions. The mean number of limited activities was 6.84 (95% confidence interval: 6.48-7.20) for persons with dementia-related limitations and 4.87 (95% confidence interval: 4.81-4.93) for those with limitations not dementia related. Both groups reported similar prevalence of diabetes, acute myocardial infarction, heart disease, prostate cancer, breast cancer, angina, and emphysema; respondents with dementia-related functional limitations were more likely to report diabetes, depression or anxiety, and vision problems as being related to functional limitations. Persons with dementia-related functional limitations were also more likely than persons with non-dementia-related functional limitations to report feeling sad, hopeless, worthless, nervous, and that "everything is an effort." Improving or maintaining functional independence in patients with dementia will likely require a multifaceted approach across disease states. Additional research will help define the impact of dementia on the development and progression of functional limitations related to comorbidities.
2012-03-13
... Northeastern United States; Northeast Multispecies Fishery; Trip Limit Adjustments for the Common Pool Fishery... GB cod is 205,030 lb (93 mt). The initial FY 2011 trip limit for GB cod was 2,000 lb (907.2 kg) per day-at-sea (DAS), up to 20,000 lb (9,071.8 kg) per trip, for Category A DAS vessels. However, the...
Fatigue and Serviceability Limit State Model Basis for Assessment of Offshore Wind Energy Converters
DEFF Research Database (Denmark)
Thons, S.; Faber, M. H.; Rücker, W.
2012-01-01
This paper develops the models for the structural performance of the loading and probabilistic characterization for the fatigue and the serviceability limit states for the support structure of offshore wind energy converters. These models and a sensitivity study are part of a risk based assessment...... al. ("Ultimate Limit State Model Basis for Assessment of Offshore Wind Energy Con-verters," ASME J. Offshore Mech. Arct. Eng.), the model basis for the assessment is completed. The process of establishing and analyzing such a model basis contributes to a detailed understanding of the deterministic...
Practical limitation for continuous-variable quantum cryptography using coherent States.
Namiki, Ryo; Hirano, Takuya
2004-03-19
In this Letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise.
Energy Technology Data Exchange (ETDEWEB)
Nenov, Artur, E-mail: Artur.Nenov@unibo.it; Giussani, Angelo; Segarra-Martí, Javier; Jaiswal, Vishal K. [Dipartimento di Chimica “G. Ciamician,” Università di Bologna, Via Selmi 2, IT-40126 Bologna (Italy); Rivalta, Ivan [Université de Lyon, CNRS, Institut de Chimie de Lyon, École Normale Supérieure de Lyon, 46 Allée d’Italie, F-69364 Lyon Cedex 07 (France); Cerullo, Giulio [Dipartimento di Fisica, Politecnico di Milano, IFN-CNR, Piazza Leonardo Da Vinci 32, IT-20133 Milano (Italy); Mukamel, Shaul [Department of Chemistry, University of California, Irvine, California 92697-2025 (United States); Garavelli, Marco, E-mail: marco.garavelli@unibo.it, E-mail: marco.garavelli@ens-lyon.fr [Dipartimento di Chimica “G. Ciamician,” Università di Bologna, Via Selmi 2, IT-40126 Bologna (Italy); Université de Lyon, CNRS, Institut de Chimie de Lyon, École Normale Supérieure de Lyon, 46 Allée d’Italie, F-69364 Lyon Cedex 07 (France)
2015-06-07
Pump-probe electronic spectroscopy using femtosecond laser pulses has evolved into a standard tool for tracking ultrafast excited state dynamics. Its two-dimensional (2D) counterpart is becoming an increasingly available and promising technique for resolving many of the limitations of pump-probe caused by spectral congestion. The ability to simulate pump-probe and 2D spectra from ab initio computations would allow one to link mechanistic observables like molecular motions and the making/breaking of chemical bonds to experimental observables like excited state lifetimes and quantum yields. From a theoretical standpoint, the characterization of the electronic transitions in the visible (Vis)/ultraviolet (UV), which are excited via the interaction of a molecular system with the incoming pump/probe pulses, translates into the determination of a computationally challenging number of excited states (going over 100) even for small/medium sized systems. A protocol is therefore required to evaluate the fluctuations of spectral properties like transition energies and dipole moments as a function of the computational parameters and to estimate the effect of these fluctuations on the transient spectral appearance. In the present contribution such a protocol is presented within the framework of complete and restricted active space self-consistent field theory and its second-order perturbation theory extensions. The electronic excited states of adenine have been carefully characterized through a previously presented computational recipe [Nenov et al., Comput. Theor. Chem. 1040–1041, 295-303 (2014)]. A wise reduction of the level of theory has then been performed in order to obtain a computationally less demanding approach that is still able to reproduce the characteristic features of the reference data. Foreseeing the potentiality of 2D electronic spectroscopy to track polynucleotide ground and excited state dynamics, and in particular its expected ability to provide
A separated bias identification and state estimation algorithm for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
Switching between bistable states in a discrete nonlinear model with long-range dispersion
DEFF Research Database (Denmark)
Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth
1998-01-01
In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...
Modal control of unstable boiling states in three-dimensional nonlinear pool-boiling
van Gils, R.W.; Speetjens, M.F.M; Zwart, Heiko J.; Nijmeijer, H.
2014-01-01
Topic is feedback stabilisation of a nonlinear pool-boiling system in three spatial dimensions (3D). Regulation of its unstable (non-uniform) equilibria has great potential for application in micro-electronics cooling and thermal-management systems. Here, as a first step, stabilisation of such 3D
Modal control of unstable boiling states in three-dimensional nonlinear pool-boiling
Gils, van R.W.; Speetjens, M.F.M; Zwart, H.J.; Nijmeijer, H.
2014-01-01
Topic is feedback stabilisation of a nonlinear pool-boiling system in three spatial dimensions (3D). Regulation of its unstable (non-uniform) equilibria has great potential for application in micro-electronics cooling and thermal-management systems. Here, as a first step, stabilisation of such 3D eq
Directory of Open Access Journals (Sweden)
Teresa D'Aprile
2000-11-01
Full Text Available In this paper we study the existence of concentrated solutions of the nonlinear field equation $$ -h^{2}Delta v+V(xv-h^{p}Delta_{p}v+ W'(v=0,, $$ where $v:{mathbb R}^{N}o{mathbb R}^{N+1}$, $Ngeq 3$, $p>N$, the potential $V$ is positive and radial, and $W$ is an appropriate singular function satisfying a suitable symmetric property. Provided that $h$ is sufficiently small, we are able to find solutions with a certain spherical symmetry which exhibit a concentration behaviour near a circle centered at zero as $ho 0^{+}$. Such solutions are obtained as critical points for the associated energy functional; the proofs of the results are variational and the arguments rely on topological tools. Furthermore a penalization-type method is developed for the identification of the desired solutions.
Chu-Tong Wang; Tsai, Jason S. H.; Chia-Wei Chen; You Lin; Shu-Mei Guo; Leang-San Shieh
2010-01-01
An active fault-tolerant pulse-width-modulated tracker using the nonlinear autoregressive moving average with exogenous inputs model-based state-space self-tuning control is proposed for continuous-time multivariable nonlinear stochastic systems with unknown system parameters, plant noises, measurement noises, and inaccessible system states. Through observer/Kalman filter identification method, a good initial guess of the unknown parameters of the chosen model is obtained so as to reduce the ...
Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state
Wang, Qi'ang; Wu, Ziyan; Liu, Shukui
2012-03-01
Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multispan continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.
Physical limitations to the spatial resolution of solid-state detectors
Boronat, M; Frey, A; Garcia, I; Schwenker, B; Vos, M; Wilk, F
2015-01-01
In this paper we explore the effect of -ray emission and fluctuations in the signal deposition on the detection of charged particles in silicon-based detectors. We show that these two effects ultimately limit the resolution that can be achieved by interpolation of the signal in finely segmented position-sensitive solid-state devices.
2011-08-30
... National Oceanic and Atmospheric Administration 50 CFR Part 648 RIN 0648-XA652 Fisheries of the Northeastern United States; Northeast Multispecies Fishery; Trip Limit Decrease for the Common Pool Fishery AGENCY: National Marine Fisheries Service (NMFS), National Oceanic and Atmospheric Administration...
Ultimate Limit State Model Basis for Assessment of Offshore Wind Energy Converters
DEFF Research Database (Denmark)
Thöns, S.; Faber, M. H.; Rücker, W.
2012-01-01
This paper establishes the model basis regarding the ultimate limit state consisting of structural, loading, and probabilistic models of the support structure of offshore wind energy converters together with a sensitivity study. The model basis is part of a risk based assessment and monitoring...
DEFF Research Database (Denmark)
Hansen, Anders Kragh; Jensen, Ole Bjarlin; Sumpf, Bernd
2014-01-01
-focusing and dispersion compensating optics between the two nonlinear crystals. In the low-power limit, such a cascade of two crystals has the theoretical potential for generation of four times as much power as a single crystal without adding significantly to the complexity of the system. The experimentally achieved...... frequency conversion of infrared tapered diode lasers. Here, we describe the generation of 3.5 W of diffraction-limited green light from SHG of a single tapered diode laser, itself yielding 10 W at 1063 nm. This SHG is performed in single pass through a cascade of two PPMgO:LN crystals with re...... power of 3.5 W corresponds to a power enhancement greater than 2 compared to SHG in each of the crystals individually and is the highest visible output power generated by frequency conversion of a single diode laser. Such laser sources provide the necessary pump power for biophotonics applications...
Features and states of microscopic particles in nonlinear quantum-mechanics systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can
Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
Brockmann, M.; De Nardis, J.; Wouters, B.; Caux, J.-S.
2014-08-01
We specialize a recently-proposed determinant formula (Brockmann, De Nardis, Wouters and Caux 2014 J. Phys. A: Math. Theor. 47 145003) for the overlap of the zero-momentum Néel state with Bethe states of the spin-1/2 XXZ chain to the case of an odd number of downturned spins, showing that it is still of ‘Gaudin-like’ form, similar to the case of an even number of down spins. We generalize this result to the overlap of q-raised Néel states with parity-invariant Bethe states lying in a nonzero magnetization sector. The generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the Lieb-Liniger (LL) Bose gas. The odd number of down spins directly translates to an odd number of bosons. We furthermore give a proof that the Néel state has no overlap with non-parity-invariant Bethe states. This is based on a determinant expression for overlaps with general Bethe states that was obtained in the context of the XXZ chain with open boundary conditions (Pozsgay 2013 arXiv:1309.4593, Kozlowski and Pozsgay 2012 J. Stat. Mech. P05021, Tsuchiya 1998 J. Math. Phys. 39 5946). The statement that overlaps with non-parity-invariant Bethe states vanish is still valid in the scaling limit to LL which means that the Bose-Einstein condensate state (De Nardis, Wouters, Brockmann and Caux 2014 Phys. Rev. A 89 033601) has zero overlap with non-parity-invariant LL Bethe states.
Improved Limits on $B^{0}$ Decays to Invisible $(+gamma)$ Final States
Energy Technology Data Exchange (ETDEWEB)
Lees, J.P.; Poireau, V.; Tisserand, V.; /Annecy, LAPP; Garra Tico, J.; Grauges, E.; /Barcelona U., ECM; Palano, A.; /Bari U. /INFN, Bari; Eigen, G.; Stugu, B.; /Bergen U.; Brown, David Nathan; Kerth, L.T.; Kolomensky, Yu.G.; Lynch, G.; /LBL, Berkeley /UC, Berkeley; Koch, H.; Schroeder, T.; /Ruhr U., Bochum; Asgeirsson, D.J.; Hearty, C.; Mattison, T.S.; McKenna, J.A.; So, R.Y.; /British Columbia U.; Khan, A.; /Brunel U.; Blinov, V.E.; /Novosibirsk, IYF /UC, Irvine /UC, Riverside /UC, Santa Barbara /UC, Santa Cruz /Caltech /Cincinnati U. /Colorado U. /Colorado State U. /Dortmund U. /Dresden, Tech. U. /Ecole Polytechnique /Edinburgh U. /Ferrara U. /INFN, Ferrara /Frascati /Genoa U. /INFN, Genoa /Indian Inst. Tech., Guwahati /Harvard U. /Harvey Mudd Coll. /Heidelberg U. /Humboldt U., Berlin /Imperial Coll., London /Iowa State U. /Iowa State U. /Johns Hopkins U. /Orsay, LAL /LLNL, Livermore /Liverpool U. /Queen Mary, U. of London /Royal Holloway, U. of London /Louisville U. /Mainz U., Inst. Kernphys. /Manchester U., Comp. Sci. Dept. /Maryland U. /Massachusetts U., Amherst /MIT /McGill U. /Milan U. /INFN, Milan /Mississippi U. /Montreal U. /Naples U. /INFN, Naples /NIKHEF, Amsterdam /Notre Dame U. /Ohio State U.; /more authors..
2013-11-01
We establish improved upper limits on branching fractions for B{sup 0} decays to final states where the decay products are purely invisible (i.e., no observable final state particles) and for final states where the only visible product is a photon. Within the Standard Model, these decays have branching fractions that are below the current experimental sensitivity, but various models of physics beyond the Standard Model predict significant contributions for these channels. Using 471 million B{bar B} pairs collected at the {Upsilon} (4S) resonance by the BABAR experiment at the PEP-II e{sup +}e{sup -} storage ring at the SLAC National Accelerator Laboratory, we establish upper limits at the 90% confidence level of 2.4 x 10{sup -5} for the branching fraction of B{sup 0} {yields} invisible and 1.7 x 10{sup -5} for the branching fraction of B{sup 0} {yields} invisible + {gamma}.
Investigation of Concrete Structures in Serviceability Limit State Using Energy Principles
DEFF Research Database (Denmark)
Hagsten, Lars German; Fisker, Jakob
2013-01-01
In this paper, a method concerning analysis of reinforced concrete structures in the serviceability limit state (SLS) is discussed. The method is based on elastic energy principles, combined with simple assumptions with respect to concrete mechanics. This approach allows for a direct implementati...... the choices made regarding the ULS and the state of stress in the SLS is compared with tests on reinforced concrete disks and beams, respectively. Fairly good agreement between theory and tests is achieved.......In this paper, a method concerning analysis of reinforced concrete structures in the serviceability limit state (SLS) is discussed. The method is based on elastic energy principles, combined with simple assumptions with respect to concrete mechanics. This approach allows for a direct implementation...
Improved Limits on $B^{0}$ Decays to Invisible $(+gamma)$ Final States
Energy Technology Data Exchange (ETDEWEB)
Lees, J.P.; Poireau, V.; Tisserand, V.; /Annecy, LAPP; Garra Tico, J.; Grauges, E.; /Barcelona U., ECM; Palano, A.; /Bari U. /INFN, Bari; Eigen, G.; Stugu, B.; /Bergen U.; Brown, David Nathan; Kerth, L.T.; Kolomensky, Yu.G.; Lynch, G.; /LBL, Berkeley /UC, Berkeley; Koch, H.; Schroeder, T.; /Ruhr U., Bochum; Asgeirsson, D.J.; Hearty, C.; Mattison, T.S.; McKenna, J.A.; So, R.Y.; /British Columbia U.; Khan, A.; /Brunel U.; Blinov, V.E.; /Novosibirsk, IYF /UC, Irvine /UC, Riverside /UC, Santa Barbara /UC, Santa Cruz /Caltech /Cincinnati U. /Colorado U. /Colorado State U. /Dortmund U. /Dresden, Tech. U. /Ecole Polytechnique /Edinburgh U. /Ferrara U. /INFN, Ferrara /Frascati /Genoa U. /INFN, Genoa /Indian Inst. Tech., Guwahati /Harvard U. /Harvey Mudd Coll. /Heidelberg U. /Humboldt U., Berlin /Imperial Coll., London /Iowa State U. /Iowa State U. /Johns Hopkins U. /Orsay, LAL /LLNL, Livermore /Liverpool U. /Queen Mary, U. of London /Royal Holloway, U. of London /Louisville U. /Mainz U., Inst. Kernphys. /Manchester U., Comp. Sci. Dept. /Maryland U. /Massachusetts U., Amherst /MIT /McGill U. /Milan U. /INFN, Milan /Mississippi U. /Montreal U. /Naples U. /INFN, Naples /NIKHEF, Amsterdam /Notre Dame U. /Ohio State U.; /more authors..
2013-11-01
We establish improved upper limits on branching fractions for B{sup 0} decays to final states where the decay products are purely invisible (i.e., no observable final state particles) and for final states where the only visible product is a photon. Within the Standard Model, these decays have branching fractions that are below the current experimental sensitivity, but various models of physics beyond the Standard Model predict significant contributions for these channels. Using 471 million B{bar B} pairs collected at the {Upsilon} (4S) resonance by the BABAR experiment at the PEP-II e{sup +}e{sup -} storage ring at the SLAC National Accelerator Laboratory, we establish upper limits at the 90% confidence level of 2.4 x 10{sup -5} for the branching fraction of B{sup 0} {yields} invisible and 1.7 x 10{sup -5} for the branching fraction of B{sup 0} {yields} invisible + {gamma}.
State estimation of nonlinear stochastic systems using a novel meta-heuristic particle filter
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Izadi-Zamanabadi, Roozbeh
2012-01-01
This paper proposes a new version of the particle filtering (PF) algorithm based on the invasive weed optimization (IWO) method. The sub-optimality of the sampling step in the PF algorithm is prone to estimation errors. In order to avert such approximation errors, this paper suggests applying...... the IWO algorithm by translating the sampling step into a nonlinear optimization problem. By introducing an appropriate fitness function, the optimization problem is properly treated. The validity of the proposed method is evaluated against three distinct examples: the stochastic volatility estimation...... problem in finance, the severely nonlinear waste water sludge treatment plant, and the benchmark target tracking on re-entry problem. By simulation analysis and evaluation, it is verified that applying the suggested IWO enhanced PF algorithm (PFIWO) would contribute to significant estimation performance...
Generation of Photon-Plasmon Quantum States in Nonlinear Hyperbolic Metamaterials
Poddubny, Alexander N.; Iorsh, Ivan V.; Sukhorukov, Andrey A.
2016-09-01
We develop a general theoretical framework of integrated paired photon-plasmon generation through spontaneous wave mixing in nonlinear plasmonic and metamaterial nanostructures, rigorously accounting for material dispersion and losses in quantum regime through the electromagnetic Green function. We identify photon-plasmon correlations in layered metal-dielectric structures with 70% internal heralding quantum efficiency, and reveal novel mechanism of broadband generation enhancement due to topological transition in hyperbolic metamaterials.
Understanding of Materials State and its Degradation using Non-Linear Ultrasound (NLU) Approaches
2011-07-01
at Ultrasonic Frequencies, Journal of Applied Physics 105, 043520, Hikata A., Chick B. B., and Elbaum C., (1965) Dislocation Contribution to the...Second Harmonic Generation of ultrasonic waves, Journal of Applied Physics Vol. 36 Number1 Hikata A. and Elbaum C., (1966) Generation of...Material Damage in a Nickel-base Superalloy using Nonlinear Rayleigh Surface Waves, Journal of Applied Physics 99, 124913 Hurley D. C., Balzar D
Institute of Scientific and Technical Information of China (English)
Zongyao SUN; Yungang LIU
2007-01-01
In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper,without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.
Cheng, Hongxia; Dong, Ningning; Bai, Ting; Song, Yi; Wang, Jun; Qin, Yuanhao; Zhang, Bin; Chen, Yu
2016-03-18
New soluble MoS2 nanosheets covalently functionalized with poly(N-vinylcarbazole) (MoS2-PVK) were in situ synthesized for the first time. In contrast to MoS2 and MoS2 /PVK blends, both the solution of MoS2 -PVK in DMF and MoS2-PVK/poly(methyl methacrylate) (PMMA) film show superior nonlinear optical and optical limiting responses. The MoS2-PVK/PMMA film shows the largest nonlinear coefficients (βeff) of about 917 cm GW(-1) at λ=532 nm (cf. 100.69 cm GW(-1) for MoS2/PMMA and 125.12 cm GW(-1) for MoS2/PVK/PMMA) and about 461 cm GW(-1) at λ=1064 nm (cf. -48.92 cm GW(-1) for MoS2/PMMA and 147.56 cm GW(-1) for MoS2/PVK/PMMA). A larger optical limiting effect, with thresholds of about 0.3 GW cm(-2) at λ=532 nm and about 0.5 GW cm(-2) at λ=1064 nm, was also achieved from the MoS2-PVK/PMMA film. These values are among the highest reported for MoS2-based nonlinear optical materials. These results show that covalent functionalization of MoS2 with polymers is an effective way to improve nonlinear optical responses for efficient optical limiting devices.
Olivier, Michel; Gagnon, Marc-Daniel; Piché, Michel
2015-03-09
A strategy to align a mode-locked fiber laser with nonlinear polarization rotation is presented. This strategy is based on measurements of the output polarization state. It is shown that, as the angle of a motorized polarization controller inside the cavity is swept, the laser eventually reaches a mode-locked regime and the values of the Stokes parameters undergo an abrupt change. The sensing of this sudden variation is thus used to detect the mode-locking condition and a feedback mechanism drives the alignment of the polarization controller to force mode locking.
Pareto-Optimal Evaluation of Ultimate Limit States in Offshore Wind Turbine Structural Analysis
Directory of Open Access Journals (Sweden)
Michael Muskulus
2015-12-01
Full Text Available The ultimate capacity of support structures is checked with extreme loads. This is straightforward when the limit state equations depend on a single load component, and it has become common to report maxima for each load component. However, if more than one load component is influential, e.g., both axial force and bending moments, it is not straightforward how to define an extreme load. The combination of univariate maxima can be too conservative, and many different combinations of load components can result in the worst value of the limit state equations. The use of contemporaneous load vectors is typically non-conservative. Therefore, in practice, limit state checks are done for each possible load vector, from each time step of a simulation. This is not feasible when performing reliability assessments and structural optimization, where additional, time-consuming computations are involved for each load vector. We therefore propose to use Pareto-optimal loads, which are a small set of loads that together represent all possible worst case scenarios. Simulations with two reference wind turbines show that this approach can be very useful for jacket structures, whereas the design of monopiles is often governed by the bending moment only. Even in this case, the approach might be useful when approaching the structural limits during optimization.
Investigation of Limit States Specified for Reinforced Concrete Column Members in TEC–2007
Directory of Open Access Journals (Sweden)
Umut HASGÜL
2016-01-01
Full Text Available In this study, the deformation based limit states stipulated for reinforced concrete members in the Turkish Earthquake Code (TEC were experimentally investigated. Thus four RC cantilever columns which have low concrete compressive strengths and have not adequate confinement, were subjected to constant axial load and cyclic lateral load history. In the study, firstly, the strain values representing the damage limits were converted to top of the column lateral displacements by using fundamentals of structural mechanics. Subsequently the column damages corresponding to the displacement demands were observed, hence limit states were evaluated. After conducting all column tests, it was noted that no column damage was observed for the immediate occupancy (IO performance level defined in the code. For the life safety (LS and collapse prevention (CP performance levels, though somewhat residual deformations occurred on the critical regions, the column members can pretty much sustain their lateral load capacities. It was also observed for all columns that significant damages and strength losses occurred beyond the collapse prevention level. The results of experimental study indicate that the evaluation procedure in the TEC is still in good relationship with the limit states even if the columns have not adequate compressive strength and confinement.
DETERMINATION OF THE TIME LIMITS OF ELIGIBILITY IN A STATE OF EXTREME NECESSITY
Directory of Open Access Journals (Sweden)
Vyacheslav Victorovich Naumov
2015-12-01
Full Text Available Up to now the limits of eligibility of extreme necessity were not the subject of independent research.The problems of definition of the time limits of p eligibility are considered in this article based on the scientific and monographic literature analysis. Relevance of the considered matter is defined by the fact that the correct establishment of time limits of eligibility of act is of great importance in the law enforcement activity in order to establish the non-delinquency of act in state of extreme necessity. The purpose of this research is the analysis of definition of time limits of extreme necessity eligibility and drawing proposals on this basis for improvement of legislative regulations and existing laws enforcement efficiency with regards to extreme necessity. Research methods: dialectic, formal-logical, system. The author empha-sizes the eligibility limits of admissible harm and the temporary limits. When determining the time limits the author emphasizes the following criteria: the value of danger, intensity of actions, and also identifies an "initial" and "final" moments in the defense of legally protected interests. The improvement of the existing legisla-tion was proposed based on the carried-out analysis.
Series transformer based diode-bridge-type solid state fault current limiter
Institute of Scientific and Technical Information of China (English)
Amir HEIDARY; Hamid RADMANESH; Seyed Hamid FATHI; G B GHAREHPETIAN
2015-01-01
We propose a novel series transformer based diode-bridge-type solid state fault current limiter (SSFCL). To control the fault current, a series RLC branch is connected to the secondary side of an isolation series transformer. Based on this RLC branch, two current limiting modes are created. In the first mode, R and C are bypassed via a paralleled power electronic switch (insulated-gate bipolar transistor, IGBT) and L remains connected to the secondary side of the transformer as a DC reactor. In the second mode, the series reactor impedance is not enough to limit the fault current. In this case, the fault current can be con-trolled by selecting a proper on-off duration of the parallel IGBT, across the series damping resistor (R) and capacitor, which inserts high impedance into the line to limit the fault current. Then, by controlling the magnitude of the DC reactor current, the fault current is reduced and the voltage of the point of common coupling (PCC) is kept at an acceptable level. In addition, in the new SSFCL, the series RC branch, connected in parallel with the IGBT, serves as a snubber circuit for decreasing the transient recovery voltage (TRV) of the IGBT during on-off states. Therefore, the power quality indices can be improved. The measure-ment results of a built prototype are presented to support the simulation and theoretical studies. The proposed SSFCL can limit the fault current without any delay and successfully smooth the fault current waveform.
Abellán-Nebot, J. V.; Liu, J.; Romero, F.
2009-11-01
The State Space modelling approach has been recently proposed as an engineering-driven technique for part quality prediction in Multistage Machining Processes (MMP). Current State Space models incorporate fixture and datum variations in the multi-stage variation propagation, without explicitly considering common operation variations such as machine-tool thermal distortions, cutting-tool wear, cutting-tool deflections, etc. This paper shows the limitations of the current State Space model through an experimental case study where the effect of the spindle thermal expansion, cutting-tool flank wear and locator errors are introduced. The paper also discusses the extension of the current State Space model to include operation variations and its potential benefits.
Institute of Scientific and Technical Information of China (English)
黄思训; 项杰; 韩威
2004-01-01
The troposphere and ocean mixed layer were considered as two components of a dynamic system operated by solar radiation as the constant source of energy, where upon an air-sea coupling selfexited coupling oscillation model was based with the aid of a locally averaged thermodynamic climate model, resulting mathematically in a closed self-governed dynamic system, a so-called El Nino-Southern Oscillation (ENSO) system. With the limit cycle solution of the system. It is shown that the essential physics of the coupled system can be described by the ENSO system. Compared with the observations, the theoretical limit cycle orbit matches the observed phase loop qualitatively. The ENSO system provides a useful theoretical framework for study of interannual variation of the tropical climate system.
Classical states and decoherence by unitary evolution in the thermodynamic limit
Frasca, M
2002-01-01
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting with a spin-bath, it is seen how decoherence, with the off-diagonal terms in the density matrix going to zero, can be obtained when the number of the spins in the bath is taken to go formally to infinity. In this case, indeed, the system appears to flop at a frequency being formally infinity that, from a physical standpoint, can be proved equivalent to a time average.
Mellor, Andrew; Zia, R K P
2016-01-01
We introduce an heterogeneous nonlinear $q$-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type $q_1$ or $q_2$. While here zealots never change their opinion, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever $q_1 \
Destexhe, Alain
2009-12-01
Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not clear whether such activity states are specific to simple IF models, or if they also exist in networks where neurons are endowed with complex intrinsic properties similar to electrophysiological measurements. Here, we investigate the occurrence of AI states in networks of nonlinear IF neurons, such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We successively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. AI states can be found in each case, sometimes with surprisingly small network size of the order of a few tens of neurons. We show that the presence of LTS neurons in cortex or in thalamus, explains the robust emergence of AI states for relatively small network sizes. Finally, we investigate the role of spike-frequency adaptation (SFA). In cortical networks with strong SFA in RS cells, the AI state is transient, but when SFA is reduced, AI states can be self-sustained for long times. In thalamocortical networks, AI states are found when the cortex is itself in an AI state, but with strong SFA, the thalamocortical network displays Up and Down state transitions, similar to intracellular recordings during slow-wave sleep or anesthesia. Self-sustained Up and Down states could also be generated by two-layer cortical networks with LTS cells. These models suggest that intrinsic properties such as adaptation and low-threshold bursting activity are crucial for the genesis and control of AI states in thalamocortical networks.
Osterloh, Frank E
2014-10-02
The Shockley-Queisser analysis provides a theoretical limit for the maximum energy conversion efficiency of single junction photovoltaic cells. But besides the semiconductor bandgap no other semiconductor properties are considered in the analysis. Here, we show that the maximum conversion efficiency is limited further by the excited state entropy of the semiconductors. The entropy loss can be estimated with the modified Sackur-Tetrode equation as a function of the curvature of the bands, the degeneracy of states near the band edges, the illumination intensity, the temperature, and the band gap. The application of the second law of thermodynamics to semiconductors provides a simple explanation for the observed high performance of group IV, III-V, and II-VI materials with strong covalent bonding and for the lower efficiency of transition metal oxides containing weakly interacting metal d orbitals. The model also predicts efficient energy conversion with quantum confined and molecular structures in the presence of a light harvesting mechanism.
2010-09-27
... United States; Northeast Multispecies Fishery; Trip Limit Reductions and Gear Modifications for the...) per days-at-sea (DAS) up to 1000 lb (453.6 kg) per trip, Georges Bank (GB) yellowtail flounder to 100 lb (45.4 kg) per trip, and white hake to 100 lb (45.4 kg) per DAS up to 500 lb (226.8 kg) per trip...
Directory of Open Access Journals (Sweden)
Guoguang Wen
2014-01-01
Full Text Available This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.
Samuelson, Paul A.
1978-01-01
In the usual Darwinian case in which struggle for existence leads to density limitations on the environment's carrying capacity, R. A. Fisher's reproductive-value concept reduces to zero for every initial age group. To salvage some meaning for Fisher's notion, two variant reproductive-value concepts are defined here: an “incipient reproductive-value function,” applicable to a system's early dilute stage when density effects are still ignorable; and a “second-order penultimate reproductive-value function,” linking to a system's initial conditions near equilibrium its much later small deviations from carrying-capacity equilibrium. Also, slowly changing age-structured mortality and fertility parameters of Lotka and Mendelian mating systems are shown to suggest linear reproductive-value surrogates that provide approximations for truly nonlinear diploid and haploid models. PMID:16592600
Institute of Scientific and Technical Information of China (English)
ZHOU Ming-gang; HUANG Qi-bai; WANG Yong; XU Zhi-sheng
2007-01-01
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.
Biggs, Jason D
2009-01-01
The preceding paper describes a strategy for externally influencing the course of short-time electronic excitation transfer (EET) in molecular dimers and observing the process by nonlinear wave-packet interferometry (nl-WPI). Within a sample of isotropically oriented dimers having a specified internal geometry, a vibrational mode internal to the acceptor chromophore can be preferentially driven by electronically nonresonant impulsive stimulated Raman (or resonant infrared) excitation with a short polarized control pulse. A subsequent electronically resonant polarized pump then preferentially excites the donor, and EET ensues. Here we test both the control strategy and its spectroscopic investigation-with some sacrifice of amplitude-level detail-by calculating the pump-probe difference signal. That signal is the limiting case of the control-influenced nl-WPI signal in which the two pulses in the pump pulse-pair coincide, as do the two pulses in the probe pulse-pair. We present calculated pump-probe difference ...
Practical issues in decoy-state quantum key distribution based on the central limit theorem
Trushechkin, A. S.; Kiktenko, E. O.; Fedorov, A. K.
2017-08-01
Decoy-state quantum key distribution (QKD) is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or "finite-key effects"). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as inclusion of the failure probability of the decoy-state statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.
Squeezing the limit: quantum benchmarks for the teleportation and storage of squeezed states
Energy Technology Data Exchange (ETDEWEB)
Owari, M; Plenio, M B [Institute for Mathematical Sciences, 53 Prince' s Gate, Imperial College London, London SW7 2PG (United Kingdom); Polzik, E S; Wolf, M M [Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Oe (Denmark); Serafini, A [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)], E-mail: m.owari@imperial.ac.uk
2008-11-15
We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing s is fixed, no information about its orientation in phase space is given, and the distribution of phase-space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for s=1) is given by {radical}s/(1+s), vanishing when the degree of squeezing diverges. For mixed states, as well as for general distributions of displacements, we reduce the determination of the benchmarks to the solution of a finite-dimensional semidefinite program, which yields accurate, certifiable bounds thanks to a rigorous analysis of the truncation error. This approach may be easily adapted to more general ensembles of input states.
Tonekaboni, Behnam; Szigeti, Stuart S
2015-01-01
We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys.~Rev.~A \\textbf{90}, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivity for lower QST efficiencies, and with a sufficiently large degree of squeezing can attain near-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies. Furthermore, we use the quantum Fisher information to demonstrate the near-optimality of our scheme.
Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas
Squire, J.; Schekochihin, A. A.; Quataert, E.
2017-05-01
This work, which extends Squire et al (Astrophys. J. Lett. 2016 830 L25), explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-β plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, ‘interrupting’ the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional ‘Braginskii’ regime, for both standing and traveling waves. The focus is on simplified models in one dimension, on scales much larger than the ion gyroradius. The effect has interesting implications for the physics of magnetized turbulence in the high-β conditions that are prevalent in many astrophysical plasmas.
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
Yamasue, Kohei; Fukidome, Hirokazu; Funakubo, Kazutoshi; Suemitsu, Maki; Cho, Yasuo
2015-06-05
We investigate pristine and hydrogen-intercalated graphene synthesized on a 4H-SiC(0001) substrate by using noncontact scanning nonlinear dielectric potentiometry (NC-SNDP). Permanent dipole moments are detected at the pristine graphene-SiC interface. These originate from the covalent bonds of carbon atoms of the so-called buffer layer to the substrate. Hydrogen intercalation at the interface eliminates these covalent bonds and the original quasi-(6×6) corrugation, which indicates the conversion of the buffer layer into a second graphene layer by the termination of Si bonds at the interface. NC-SNDP images suggest that a certain portion of the Si dangling bonds remains even after hydrogen intercalation. These bonds are thought to act as charged impurities reducing the carrier mobility in hydrogen-intercalated graphene on SiC.
Yamasue, Kohei; Fukidome, Hirokazu; Funakubo, Kazutoshi; Suemitsu, Maki; Cho, Yasuo
2015-06-01
We investigate pristine and hydrogen-intercalated graphene synthesized on a 4 H -SiC (0001 ) substrate by using noncontact scanning nonlinear dielectric potentiometry (NC-SNDP). Permanent dipole moments are detected at the pristine graphene-SiC interface. These originate from the covalent bonds of carbon atoms of the so-called buffer layer to the substrate. Hydrogen intercalation at the interface eliminates these covalent bonds and the original quasi-(6 ×6 ) corrugation, which indicates the conversion of the buffer layer into a second graphene layer by the termination of Si bonds at the interface. NC-SNDP images suggest that a certain portion of the Si dangling bonds remains even after hydrogen intercalation. These bonds are thought to act as charged impurities reducing the carrier mobility in hydrogen-intercalated graphene on SiC.
Wu, Xiaomao; Schelly, Z. A.; Vastano, John A.
1994-07-01
Results of studies of the limited Explodator model in a continuous-flow stirred tank reactor (CSTR) under square wave perturbation of the flow rate are reported. The perturbation is applied in such a way that the system is alternately attracted to two different periodic attractors in the parameter region close the Hopf bifurcation point. The system is shown to display a variety of entrainment bands, birhythmicity, quasiperiodicity, resonance-like phenomenon, period doubling and intermittency routes to chaos, and a complicated window structure of the chaotic region. In addition, a novel phenomenon, “intermittent alternative laminar oscillations”, was observed in a chaotic regime sandwiched between two entrainment bands. Transient chaos occurs in one of the entrainment bands, which intimates chaos in the adjacent regime. Positive Lyapunov exponents were found to be associated with the chaotic behavior. The folding and stretching property of the chaotic attractors was analyzed through stroboscopic representations. The deterministic nature of the chaotic behavior was confirmed by the quadratic-like curve formed in the one-dimensional map.
78 FR 70414 - Pricing for the 2013 United States Mint Limited Edition Silver Proof SetTM
2013-11-25
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF THE TREASURY United States Mint Pricing for the 2013 United States Mint Limited Edition Silver Proof Set TM AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint...
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner
2017-07-01
A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.
Highly enhanced steady-state optomechanical entanglement via cross-Kerr nonlinearity
Chakraborty, Subhadeep
2016-01-01
We study steady-state optomechanical entanglement in presence of an additional cross-Kerr coupling between the optical and mechanical mode. We find that a significant enhancement of the steady-state entanglement can be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature.
Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.
Zhang, Bin W; Dai, Wei; Gallicchio, Emilio; He, Peng; Xia, Junchao; Tan, Zhiqiang; Levy, Ronald M
2016-08-25
Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.
Mapping the Coastline Limits of the Mexican State Sinaloa Using GPS
Vazquez, G. E.
2007-12-01
This research work presents the delimitation of the coastline limits of Sinaloa (one of the richest states of northwestern Mexico). In order to achieve this big task, it was required to use GPS (Global Positioning System) together with leveling spirit measurements. Based on the appropriate selection of the cited measurement techniques, the objective was to map the Sinaloa's state coastline to have the cartography of approximate 1600 km of littoral. The GPS measurements were performed and referred with respect to a GPS network located across the state. This GPS network consists of at least one first-order-site at each of the sixteen counties that constitute the state, and three to four second-order-sites of the ten counties of the state surrounded by sea. The leveling spirit measurements were referred to local benchmarks pre-established by the Mexican agency SEMARNAT (SEcretaría Del Medio Ambiente y Recursos NATurales). Within the main specifications of the GPS measurements and equipment, we used geodetic-dual-frequency GPS receivers in kinematic mode for both base stations (first and second order sites of the GPS state network) and rover stations (points forming the state littoral) with 5-sec log-rate interval and 10 deg cut-off angle. The GPS data processing was performed using the commercial software Trimble Geomatics Office (TGO) with Double Differences (DD) in post-processing mode. To this point, the field measurements had been totally covered including the cartography (scale 1:1000) and this includes the specifications and appropriate labeling according to the Mexican norm NOM-146-SEMARNAT-2005.
Dreano, D.
2017-04-05
Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.
Can quantum transition state theory be defined as an exact t = 0+ limit?
Jang, Seogjoo; Voth, Gregory A
2016-02-28
The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown
Absorption spectroscopy at the ultimate quantum limit from single-photon states
Whittaker, R.; Erven, C.; Neville, A.; Berry, M.; O’Brien, J. L.; Cable, H.; Matthews, J. C. F.
2017-02-01
Absorption spectroscopy is routinely used to characterise chemical and biological samples. For the state-of-the-art in laser absorption spectroscopy, precision is theoretically limited by shot-noise due to the fundamental Poisson-distribution of photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use wavelength-correlated and tuneable photon pairs to demonstrate how absorption spectroscopy can be performed with precision beyond the shot-noise limit and near the ultimate quantum limit by using the optimal probe for absorption measurement—single photons. We present a practically realisable scheme, which we characterise both the precision and accuracy of by measuring the response of a control feature. We demonstrate that the technique can successfully probe liquid samples and using two spectrally similar types of haemoglobin we show that obtaining a given precision in resolution requires fewer heralded single probe photons compared to using an idealised laser.
Racial Disparities in Functional Limitations Among Hispanic Women in the United States.
Chinn, Juanita J; Hummer, Robert A
2016-04-01
This article assesses whether there are race differences in functional health among Hispanic women in the United States; ascertains whether the race differences in functional health vary by age; and examines the extent to which race differences in functional health are attributable to key dimensions of demographic, geographic, and socioeconomic heterogeneity. The analysis is based on 15 years of aggregated data from the National Health Interview Survey. Both U.S.- and foreign-born Black and other race Hispanic women display a higher level of functional limitations than their White Hispanic counterparts. There is little evidence that such health differences widen with age. U.S.-born Black Hispanic women, however, suffer from a high burden of functional limitations across the adult age range. This research speaks to the need for greater attention to racial differences in health among Hispanics and particularly so within the U.S.-born segment of this rapidly aging population. © The Author(s) 2015.
Steady-state analysis of the effect of reactive generation limits in voltage stability
Energy Technology Data Exchange (ETDEWEB)
Echavarren, F.M.; Lobato, E.; Rouco, L. [School of Engineering of Universidad Pontificia Comillas, C/Alberto Aguilera, 23, 28015 Madrid (Spain)
2009-09-15
Voltage collapse phenomena are highly affected by reactive power generation limits. Saturation of the reactive power generation limits of a unit may result in a deterioration of the voltage stability. However, in some cases when the power network is operating close to the voltage collapse point, the reactive power generation saturation of a unit can change the system voltages immediately from stable to unstable; thus, a dynamic voltage collapse leading to blackout may follow. This paper presents a steady-state analysis of the immediate instability caused by reactive power generation saturation phenomena. For this purpose, the paper proposes a novel index that evaluates ''when'' and ''why'' a reactive power generation saturation will only result in a deterioration of the system voltage stability or, on the contrary, it will make the system voltages immediately unstable. (author)
Elavarasu, N.; Sathya, P.; Pugazhendhi, S.; Vijayan, N.; Maurya, K. K.; Gopalakrishnan, R.
2016-10-01
Ammonium D,L-Tartrate (AMT) single crystal for optical and photonic device application was analyzed with different characterization studies. The AMT crystal was grown by low cost conventional solution growth technique. The unit cell parameters were obtained from single crystal XRD analysis and the crystal system is confirmed to be orthorhombic with noncentrosymmetric space group P212121. The crystalline perfection evaluated by high resolution X-ray diffractometry (HRXRD) enumerates the quality of the crystal is good. The optical transparency window of AMT crystal has 78% transmittance from 234 nm to 1100 nm region and has lower cut-off wavelength of 234 nm was analyzed by UV-visible spectral studies. The hardness number (Hv), yield strength (σy) and elastic stiffness constant (C11) were evaluated from the hardness data using Vickers hardness tester. Dielectric study indicates the moderate dielectric constant and low dielectric loss of AMT crystal which are required properties to develop optoelectronic devices. The laser damage threshold value of AMT is 0.238 GW/cm2 and photoconductivity study reveals the positive photoconductivity nature of the AMT crystal. The particle size dependent SHG studies were performed using Nd:YAG laser. The SHG efficiency of AMT is found to be 1.3 times greater than the standard KDP crystal. Third order nonlinear susceptibility χ(3) of AMT was assessed using an open aperture and closed aperture Z-scan technique and the value is 6.71×10-6 esu. AMT crystal is found to exhibit good optical power limiting. The present work indicates that AMT is a potential material for optoelectronic and nonlinear optical devices.
Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit
Lei, C. U.; Weinstein, A. J.; Suh, J.; Wollman, E. E.; Kronwald, A.; Marquardt, F.; Clerk, A. A.; Schwab, K. C.
2016-09-01
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe 4.7 ±0.9 dB of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.
Capabilities, limitations and challenges of a simplified PC-SAFT equation of state
DEFF Research Database (Denmark)
von Solms, Nicolas; Kouskoumvekaki, Irene; Michelsen, Michael Locht
2006-01-01
and physical performance of a modified PC-SAFT equation of state for highly asymmetric and associating mixtures, Ind. Eng. Chem. Res. 42 (2003) 1098.] has been applied to several complex polymer-sol vent systems, including vapor-liquid equilibria, liquid-liquid equilibria and gas solubilities for both single-solvent...... and mixed-solvents (ternary) systems. This manuscript briefly reviews previous successful applications of PC-SAFT, illustrates the capabilities of the model and indicates some problems and limitations in specific areas, especially aqueous systems and blends, as well as challenges that need to be addressed...
Shortell, Matthew P; Jaatinen, Esa A; Chang, Jin; Waclawik, Eric R
2014-03-24
We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.
Bulgakov, Evgeny; Pichugin, Konstantin; Sadreev, Almas
2013-10-01
We show that two nonlinear resonant cavities aligned between two parallel waveguides can support self-induced bound states in the continuum (BSCs). These BSCs are symmetrical relative to an inversion of the waveguides and to inversion of the transport axis. Due to this BSCs can drop an incident wave from one waveguide to another with very high efficiency. We show also that the frequency of the efficient channel dropping can be tuned by injecting power. All these results are in good agreement with numerical solutions of the Maxwell equations in a two-dimensional photonic crystal of GaAs rods holding two parallel waveguides and two defects made of a Kerr medium.
Wen, Guoxing; Chen, C L Philip; Liu, Yan-Jun; Liu, Zhi
2016-10-11
Compared with the existing neural network (NN) or fuzzy logic system (FLS) based adaptive consensus methods, the proposed approach can greatly alleviate the computation burden because it needs only to update a few adaptive parameters online. In the multiagent agreement control, the system uncertainties derive from the unknown nonlinear dynamics are counteracted by employing the adaptive NNs; the state delays are compensated by designing a Lyapunov-Krasovskii functional. Finally, based on Lyapunov stability theory, it is demonstrated that the proposed consensus scheme can steer a multiagent system synchronizing to the predefined reference signals. Two simulation examples, a numerical multiagent system and a practical multimanipulator system, are carried out to further verify and testify the effectiveness of the proposed agreement approach.
Wang, Meiyu; Yan, Fengli; Gao, Ting
2017-08-01
We present a new scheme to provide an arbitrary four-photon polarization-entangled state, which enables the encoding of single logical qubit information into a four-qubit decoherence-free subspace robustly against collective decoherence. With the assistance of the cross-Kerr nonlinearities, a spatial entanglement gate and a polarization entanglement gate are inserted into the circuit, where the X-quadrature homodyne measurement is properly performed. According to the outcomes of homodyne measurement in the spatial entanglement process, some swap gates are inserted into the corresponding paths of the photons to swap their spatial modes. Apart from Kerr media, some basic linear optical elements are necessary, which make it feasible with current experimental techniques.
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
Nonlinear optical switching behavior in the solid state: A theoretical investigation on anils
Ségerie, Audrey
2011-09-13
The linear (π(1)) and second-order nonlinear (π(2)) optical properties of two anil crystals, [N-(4-hydroxy)-salicylidene-amino-4-(methylbenzoate) and N-(3,5-di-tert- butylsalicylidene)-4-aminopyridine, denoted 4A and 4P, respectively], as well as the optical contrasts upon switching between their enol (E) and keto (K) forms, have been investigated by combining the molecular responses calculated using quantum chemistry methods and an electrostatic interaction scheme to account for the local field effects. It is found that intermolecular interactions impact differently the K/E optical contrasts in the two systems, which illustrates the importance of the supramolecular organization on the macroscopic responses. In 4A, the surrounding effects on the (hyper)polarizabilities are similar in the enol and keto forms, leading to optical contrasts very close to those of the isolated molecule. In contrast, an enhancement of the second-order susceptibility is observed in the keto form of 4P, leading to a large π(2)(K)/π(2)(E) contrast. Moreover, the π(2)(4A)/π(2)(4P) ratio for the most stable enol forms is obtained to be in good agreement with previous experimental investigations, which supports the reliability of the computational procedure. © 2011 American Chemical Society.
The nonlinear squeezed one-photon states and their nonclassical properties
Institute of Scientific and Technical Information of China (English)
Wang Ji-Suo; Meng Xiang-Guo
2007-01-01
By virtue of the technique of integration within an ordered product (IWOP) of operators and the properties of the inverses of annihilation and creation operators of f-oscillator, this paper obtains two new types of squeezed operators and f-analogues of squeezed one-photon states, which are quite different from ones constructed by Song and Fan (Phys. Lett. A 294 (2002) 66). Subsequently, some nonclassical properties of the states are investigated in detail.
45 CFR 264.2 - What happens if a State does not comply with the five-year limit?
2010-10-01
... five-year limit? 264.2 Section 264.2 Public Welfare Regulations Relating to Public Welfare OFFICE OF... Penalties? § 264.2 What happens if a State does not comply with the five-year limit? If we determine that a... for the immediately succeeding fiscal year by five percent of the adjusted SFAG unless the State...
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2017-03-01
Bound-state vector soliton solutions for the coupled variable-coefficient higher-order nonlinear Schrödinger equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fiber, are investigated. Introducing auxiliary functions, we derive the bilinear forms and corresponding constraints on the variable coefficients. Through symbolic computation, we construct the one- and two-soliton solutions. We see that the variable coefficients in the equations affect the soliton structures. With different choices of the variable coefficients, we obtain the cubic, periodic, and parabolic solitons. Bound-state solitons and interactions are analyzed graphically.
Directory of Open Access Journals (Sweden)
Yin Hua
2015-04-01
Full Text Available Estimation of state of charge (SOC is of great importance for lithium-ion (Li-ion batteries used in electric vehicles. This paper presents a state of charge estimation method using nonlinear predictive filter (NPF and evaluates the proposed method on the lithium-ion batteries with different chemistries. Contrary to most conventional filters which usually assume a zero mean white Gaussian process noise, the advantage of NPF is that the process noise in NPF is treated as an unknown model error and determined as a part of the solution without any prior assumption, and it can take any statistical distribution form, which improves the estimation accuracy. In consideration of the model accuracy and computational complexity, a first-order equivalent circuit model is applied to characterize the battery behavior. The experimental test is conducted on the LiCoO2 and LiFePO4 battery cells to validate the proposed method. The results show that the NPF method is able to accurately estimate the battery SOC and has good robust performance to the different initial states for both cells. Furthermore, the comparison study between NPF and well-established extended Kalman filter for battery SOC estimation indicates that the proposed NPF method has better estimation accuracy and converges faster.
Directory of Open Access Journals (Sweden)
G. Forget
2015-10-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Three-Nucleon Bound States and the Wigner-SU(4) Limit
Vanasse, Jared; Phillips, Daniel R.
2017-03-01
We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory that is an expansion in powers of R/ a, with R the range of the nuclear force and a the nucleon-nucleon (N N) scattering lengths. In the Wigner-SU(4) limit, the triton and helium-3 point charge radii are equal. At NLO in the range expansion both are 1.66 fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the N N scattering lengths gives a ^3{H} point charge radius of 1.58 fm, which is remarkably close to the experimental number, 1.5978± 0.040 fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ^3{He} point charge radius we find 1.70 fm, about 4% away from the experimental value of 1.77527± 0.0054 fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties.
A composite state method for ensemble data assimilation with multiple limited-area models
Directory of Open Access Journals (Sweden)
Matthew Kretschmer
2015-04-01
Full Text Available Limited-area models (LAMs allow high-resolution forecasts to be made for geographic regions of interest when resources are limited. Typically, boundary conditions for these models are provided through one-way boundary coupling from a coarser resolution global model. Here, data assimilation is considered in a situation in which a global model supplies boundary conditions to multiple LAMs. The data assimilation method presented combines information from all of the models to construct a single ‘composite state’, on which data assimilation is subsequently performed. The analysis composite state is then used to form the initial conditions of the global model and all of the LAMs for the next forecast cycle. The method is tested by using numerical experiments with simple, chaotic models. The results of the experiments show that there is a clear forecast benefit to allowing LAM states to influence one another during the analysis. In addition, adding LAM information at analysis time has a strong positive impact on global model forecast performance, even at points not covered by the LAMs.
An FEM-Based State Estimation Approach to Nonlinear Hybrid Positioning Systems
Directory of Open Access Journals (Sweden)
Yu-Xin Zhao
2013-01-01
Full Text Available For hybrid positioning systems (HPSs, the estimator design is a crucial and important problem. In this paper, a finite-element-method- (FEM- based state estimation approach is proposed to HPS. As the weak solution of hybrid stochastic differential model is denoted by the Kolmogorov's forward equation, this paper constructs its interpolating point through the classical fourth-order Runge-Kutta method. Then, it approaches the solution with biquadratic interpolation function to obtain a prior probability density function of the state. A posterior probability density function is gained through Bayesian formula finally. In theory, the proposed scheme has more advantages in the performance of complexity and convergence for low-dimensional systems. By taking an illustrative example, numerical experiment results show that the new state estimator is feasible and has good performance than PF and UKF.
Directory of Open Access Journals (Sweden)
Irwin Yousept
2010-07-01
Full Text Available An optimal control problem arising in the context of 3D electromagnetic induction heating is investigated. The state equation is given by a quasilinear stationary heat equation coupled with a semilinear time harmonic eddy current equation. The temperature-dependent electrical conductivity and the presence of pointwise inequality state-constraints represent the main challenge of the paper. In the first part of the paper, the existence and regularity of the state are addressed. The second part of the paper deals with the analysis of the corresponding linearized equation. Some suffcient conditions are presented which guarantee thesolvability of the linearized system. The final part of the paper is concerned with the optimal control. The aim of the optimization is to find the optimal voltage such that a desired temperature can be achieved optimally. The corresponding first-order necessary optimality condition is presented.
Estimation of LISS(local input-to-state stability) properties for nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.
27 CFR 70.226 - Suspension of running of period of limitation; taxpayer outside of United States.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 2 2010-04-01 2010-04-01 false Suspension of running of... Limitations § 70.226 Suspension of running of period of limitation; taxpayer outside of United States. The running of the period of limitations on collection after assessment prescribed in 26 U.S.C. 6502...
Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-Convex Nonlinearities
Institute of Scientific and Technical Information of China (English)
KHAZAEE KOHPAR O; KHADEMLOO S
2013-01-01
This work is devoted to the existence and multiplicity properties of the grotmd state solutions of the semilinear boundary value problem-Au=λa(x)u｜u｜q-2+b(x) u ｜u｜2*-2 in a bounded domain coupled with Dirichlet boundary condition.Here 2* is the critical Sobolev exponent,and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions.Using the Nehari manifold method we prove that one can find an interval A such that there exist at least two positive solutions of the problem for λ ∈ A.
Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation
Kollmann, Robert
2013-01-01
This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the ‘pruning’ scheme of Kim, Kim, Schaumburg and Sims (2008). By contrast to particle filters, no stochastic simulations are needed for the filter here--the present method is thus much faster. In Monte Carlo e...
Parlitz, Ulrich; Luther, Stefan
2015-01-01
Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of this approach are introduced and illustrated for discrete and continuous time systems employing a filtered H\\'enon map and a R\\"ossler system.